Library · Optimization & control
What Convex & Mathematical Programming got wrong, from 104 theses
Summary written by a model from the records below: The records demonstrate that mathematical programming methods frequently encounter severe computational bottlenecks, solver timeouts, and memory exhaustion when applied to large-scale discrete or non-convex problems. Furthermore, convex relaxations often yield loose bounds or non-physical solutions, while real-time execution constraints and numerical instability routinely force practitioners to reject exact formulations in favor of heuristics or specialized baselines. These records come from graduate theses, 2021 to 2026, each labeled with its degree where the repository states it, and each links to its thesis. They were extracted by language models reading the full text, so treat each as a lead to read, not a verdict.
Plus 10 problems the authors left open, listed at the end.
Failure modes, by theses reporting them
Select a mode to jump to its records.
Integer and mixed-integer programming formulations suffer from combinatorial explosion and excessive solve times
Solvers applied to mixed-integer and discrete linear programs frequently time out, exhaust system memory, or scale exponentially when instance sizes or constraint counts increase. These computational limitations force practitioners to reject exact formulations or truncate searches before proving optimality on large networks and combinatorial problems.
Tried and failed
mixed-integer programming for friction cone constraints applied to contact-implicit trajectory optimization. Outcome: infeasible cost. Reason: required binary variables and too many assumptions to justify the computational complexity
Controlling Contact Transitions for Dynamic Robots · Penn · PhD
Tried and failed
mixed-integer linear programming optimization applied to prototype generation in neural networks. Outcome: infeasible cost. Reason: computational complexity and scalability limitations of MILP solvers
On interpretation methods for deep neural networks · Iowa State · PhD
Tried and failed
linear programming relaxation for graph optimization applied to large-scale genomic sequence graphs. Outcome: infeasible cost. Reason: LP solver ran out of memory on large problem instances with long path constraints
Algorithmic Techniques for Variant Selection in Genome Graphs · Georgia Tech · PhD
Tried and failed
mixed-integer linear programming exact solver applied to large-scale combinatorial optimization. Outcome: too slow. Reason: computational complexity scaled poorly with problem size, leading to prohibitive solve times per instance
Quantitative Methods for Omnichannel Decision-Making · EPFL · PhD
Tried and failed
direct integer programming on full path formulation applied to large-scale hub location and network routing. Outcome: worse than baseline. Reason: intractable search space resulted in large optimality gaps after hours, underperforming greedy heuristics
Service Network Design for Parcel Trucking · Georgia Tech · PhD
Tried and failed
integer linear programming formulation applied to phylogenetic tree reconciliation. Outcome: too slow. Reason: computational complexity scaled poorly on large instances exceeding execution time limits
Integer linear programming formulation for the unified duplication-loss-coalescence model · Iowa State · Master's
Tried and failed
iterative dual linear programming relaxations applied to constrained stochastic shortest path problems. Outcome: too slow. Reason: overhead of solving sequential (MI)LPs exceeded benefits when heuristic search space reduction was low
Risk-bounded Programming using Constrained, Hierarchical, Stochastic Shortest Path Problems · MIT · PhD
Tried and failed
unconstrained integer linear programming formulation applied to phylogenetic tree reconciliation. Outcome: too slow. Reason: large search space led to higher average runtimes and more timeouts than the baseline heuristic
Integer linear programming formulation for the unified duplication-loss-coalescence model · Iowa State · Master's
Tried and failed
exact integer linear programming formulation applied to real-time task priority assignment. Outcome: too slow. Reason: search space size caused solver timeouts on tightly constrained instances
Priority Assignment Algorithms for Real-Time Systems · Virginia Tech · Doctorate
Tried and failed
extensive deterministic equivalent mixed-integer programming applied to stochastic resource allocation with recourse. Outcome: too slow. Reason: computational complexity scaled poorly and solver timed out on small problem instances
Optimization models and management strategies for service operations · UT Austin · PhD
Tried and failed
LP relaxation with greedy rounding applied to binary integer linear programming scheduling. Outcome: too slow. Reason: Problem size scaling with slot count dominates execution time, yielding negligible speedup over exact solver
Proactive methods to maximize mmWave WLAN performance · Georgia Tech · PhD
Tried and failed
monolithic mixed-integer linear programming applied to joint clustering and resource allocation. Outcome: too slow. Reason: computational complexity scaled intractably with large problem instances beyond 500 nodes
Optimizing resource allocation in large communications satellite constellations · MIT · PhD
Tried and failed
heuristic warm starts in mixed-integer programming solvers applied to mixed-integer programming transit network design. Outcome: too slow. Reason: optimality gap reduction was bottlenecked by proving lower bounds rather than finding upper bounds
Incorporating Travel Behaviors into Transit Network Designs: Methods, Applications, and Extensions · Georgia Tech · PhD
Tried and failed
robust mixed-integer programming with affine decision rules applied to state-task network scheduling. Outcome: too slow. Reason: the resulting formulations scaled excessively and became computationally intractable compared to deterministic approximations
Formulations, algorithms and software for robust optimisation · Imperial · PhD
Tried and failed
mixed-integer linear programming for multi-agent planning applied to multi-robot search under uncertainty. Outcome: too slow. Reason: computational complexity scaled exponentially with longer planning horizons and increased agent count
Multi-Agent Planning Under Uncertainty · Cornell · PhD
Tried and failed
exact mixed-integer quadratic programming feature interaction selection applied to epistasis detection in genomic data. Outcome: too slow. Reason: MIQP solver failed to scale and remained stuck at linear relaxation bound on larger instances
Machine learning and optimization algorithms and their applications in agriculture · Iowa State · PhD
Considered and rejected
Considered and rejected: Rejected nonlinear programming (NLP) formulation for capacity sizing in whole-energy system optimization due to computational intractability with 14M+ constraints, choosing linear programming with discrete archetype sizing instead.
Multi-scale energy system optimisation for efficient, affordable and secure net-zero transitions · Imperial · PhD
Considered and rejected
Considered and rejected: Decided against brute-force full-basis linear programming constraint sets because constraint count scales exponentially with cluster spin count.
Tensor network investigation of frustrated Ising models · EPFL · PhD
Considered and rejected
Considered and rejected: Rejected using exact flow-based integer linear programming formulations for large Budget-PCSF instances due to severe scaling limitations with OD-pair flow variables.
Optimizing resource allocation in computational sustainability: Models, algorithms and tools · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected exact mixed-integer linear programming (Gurobi) for solving the maximum-sum submatrix backdoor problem because it was NP-hard and took several days per instance, replacing it with a greedy Kernighan-Lin heuristic
How Data Drives ML Models Performance · MIT · PhD
Considered and rejected
Considered and rejected: Rejected pure Integer Linear Programming for 200 demand points because it failed to find a solution due to memory/computational exhaustion
An Approach for Risk-Informed UAS Mission Planning in Urban Environments to Support First Responders · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected formulating shortest path start heuristic via integer programming due to overhead and edge-level decision variables conflicting with node-level formulations.
De-novo pathway discovery for multi-omics data · Tübingen · PhD
Considered and rejected
Considered and rejected: Rejected using Integer Linear Programming (ILP) solvers for smallest witness problems because transforming Boolean how-provenance into linear constraints causes exponential blowup.
Simplifying Human-in-the-loop Data Science Pipeline: Explanations, Debugging, and Data Preparation · Duke · PhD
Considered and rejected
Considered and rejected: Rejected exact integer programming solvers (e.g., branch-and-bound in Gurobi) for matching/stratification design due to exponential scaling and memory exhaustion.
Novel Stratification and Matching Methods in Observational Studies · Penn · PhD
Considered and rejected
Considered and rejected: Decided against linear-programming-based recursions and IRLS for DPCP due to poor computational scalability and lack of convergence guarantees.
Subspace Learning for Data Arising from a Union of Subspaces of High Relative Dimension · Johns Hopkins · PhD
Considered and rejected
Considered and rejected: Decided against exact bilevel programming solvers (e.g., branch-and-bound or KKT reformulation with big-M) for large-scale GEP, selecting an iterative heuristic algorithm for computational tractability.
Integration of machine learning and optimization for decision making under uncertainties with applications in agriculture and power system · Iowa State · PhD
Lost to a baseline
MCount processing time took 169.8 seconds per 100 sub-images, slower than NICE (15.9 s), OpenCFU (13.2 s), and AutoCellSeg (79.4 s) due to integer programming optimization
Novel High-throughput Technologies for Applications in Microbiology · MIT · PhD
Tried and failed
exact mixed-integer quadratic programming applied to real-time distributed resource allocation. Outcome: too slow. Reason: High computational complexity exceeds sub-second latency constraints without variable-reduction heuristics.
Grid-Aware Real-Time Control of Electric Vehicles · EPFL · PhD
Tried and failed
exact integer programming on time-space network applied to large-scale sort network scheduling. Outcome: too slow. Reason: computational complexity caused solver timeouts without finding feasible solutions on large problem instances
Sort Planning for Express Parcel Delivery Systems · Georgia Tech · PhD
Tried and failed
exact multi-vertex polygon constraints in mixed-integer programming applied to real-time geometric obstacle avoidance. Outcome: too slow. Reason: high-vertex polygon constraints dramatically increased solver latency, requiring bounding box approximations instead
Microscopic analysis of many optimizing air vehicles using high-performance computing · Georgia Tech · PhD
Tried and failed
mixed-integer programming based graph partitioning applied to heterogeneous resource allocation. Outcome: too slow. Reason: computational complexity caused solver timeouts on medium and large instances within practical limits
Demand Projection and Complex Resource Allocation Decisions on Networks · Georgia Tech · PhD
Tried and failed
semidefinite programming for Wasserstein distributionally robust optimization applied to two-stage network inventory allocation. Outcome: too slow. Reason: computational complexity scaled poorly, timing out at sample size exceeding ten
Distributionally robust solution schemes for two-stage optimization and interdiction problems under uncertainty · UT Austin · PhD
Tried and failed
exact integer linear programming schedulability testing applied to multiprocessor real-time task scheduling. Outcome: too slow. Reason: extreme computational complexity makes exact response time analysis impractical beyond 13 tasks
Priority Assignment Algorithms for Real-Time Systems · Virginia Tech · Doctorate
Considered and rejected
Considered and rejected: Rejected exact optimization and mathematical programming (JSP/DFJSP) due to NP-hard complexity making real-time scheduling intractable.
Improving patient benefits via digital modeling and AI-augmented decision support for supply chains of autologous cell-derived medical products · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected centralized Integer Linear Programming (ILP) formulation for TAoI rate control due to lack of global instantaneous knowledge and channel/mobility dynamics
Information Freshness: How To Achieve It and Its Impact On Low- Latency Autonomous Systems · Virginia Tech · Doctorate
Non-convex formulations and non-convex constraints violate structural assumptions and destroy convexity
Direct parameterizations, discrete restrictions, and nonlinear equality constraints frequently turn convex programs into non-convex problems where convexity cannot be established. Practitioners consequently reject these formulations because non-convex landscapes break descent lemmas, cause suboptimality, or prevent the application of standard convex solvers.
Tried and failed
standard quadratic programming solvers applied to discrete integer control optimization. Reason: solvers cannot handle discrete integer control constraints directly
An integrated battery unit regulation strategy · Cranfield · PhD
Tried and failed
pure state-feedback stochastic model predictive control applied to constrained motion planning under uncertainty. Reason: pure state feedback parameterization leads to non-convex optimization programs
Safe, High-performance Motion Planning Under Uncertainty for Autonomous Driving Applications · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected unconstrained QP solvers because bilinear quantum control dynamics impose nonlinear dynamical constraints, requiring Sequential Quadratic Programming (SQP).
Data-driven modeling and control of quantum dynamics · University of Washington · PhD
Considered and rejected
Considered and rejected: Rejected quadratic-form positive definite Lyapunov neural networks because they cannot be verified using Mixed-Integer Linear Programming (MILP).
Learning-enabled navigation and nonlinear control for resource constrained robots · Boston University · PhD
Considered and rejected
Considered and rejected: Rejected direct minimization of non-convex parametrized empirical constrained risk minimization (PIV) due to frequent infeasibility and non-zero duality gaps.
Constrained Learning And Inference · Penn · PhD
Considered and rejected
Considered and rejected: Rejected strict covariance equality constraint EN(I+BF)PZ(I+BF)⊤E_N⊤ = Pf - P̃N because it is non-convex and requires nonlinear programming; relaxed to an inequality semi-definite constraint.
Informed Sampling-Based Kinodynamic Motion Planning for Deterministic Systems And Stochastic Systems · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected exact mixed-integer modeling of discrete voltage regulator tap steps, using continuous relaxation in [0.9, 1.1] to maintain convex QP structure.
Fast and Scalable Power System Learning, Analysis, and Planning · Virginia Tech · Doctorate
Tried and failed
online optimization of risk allocation parameters applied to chance-constrained stochastic model predictive control. Reason: optimizing risk allocations directly online makes the convex optimization problem non-convex
Safe, High-performance Motion Planning Under Uncertainty for Autonomous Driving Applications · Georgia Tech · PhD
Tried and failed
convex optimization of information acquisition strategies applied to optimal strategy selection in testing games. Reason: The set of optimal strategies is non-convex, so convex combinations are not necessarily optimal.
Rational Inattention and a Causal Account of Program Security · Cornell · PhD
Tried and failed
exact convex optimization applied to privacy metric optimization. Reason: problem convexity could not be established under general probability spaces
A general framework of estimating information leakage for privacy and forensics problems with imperfect statistical information · Iowa State · PhD
Tried and failed
decoupling optimization from statistical estimation applied to convex function estimation and inference. Reason: requires unrealistic assumptions like strong convexity or uniqueness and obscures high-dimensional dependencies
Estimation And Inference For Convex Functions And Computational Efficiency In High Dimensional Statistics · Penn · PhD
Considered and rejected
Considered and rejected: Rejected standard convex weighted estimator beta * theta_SL + (1 - beta) * theta_L with optimal weights learned via constrained least squares, because optimal prediction error does not guarantee smaller parameter estimation error.
Optimal and Safe Semi-supervised Estimation and Inference for High-dimensional Linear Regression · Cornell · PhD
Considered and rejected
Considered and rejected: Rejected online optimization of risk allocation parameters px,i and pu,j because it results in a non-convex optimization problem.
Safe, High-performance Motion Planning Under Uncertainty for Autonomous Driving Applications · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Constrained ERM rejected for stochastic convex stationary-point finding because it fails to guarantee excess risk bounds even for function value suboptimality.
Non-convex and Interactive Learning via Stochastic Optimization · Cornell · PhD
Considered and rejected
Considered and rejected: Standard Policy Mirror Descent update argmax_{pi_theta} E[eta <Q, pi_theta> - D_h(pi_theta, pi_t)] rejected because non-convexity of Pi(Theta) breaks the three-point descent lemma.
Optimization methods for reinforcement learning: theory and applications · Oxford · PhD
Considered and rejected
Considered and rejected: Rejected using an equality constraint sqrt(β^T Σ_hat β) = τ because it results in a non-convex optimization problem
Efficient Robust Algorithms for Linear Discriminant Analysis and Sequential Matching Problems · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Restricting potential classifiers to arbitrary hypothesis classes (e.g., threshold functions) to compute benefit-of-splitting, which produced unstable/inaccurate values and non-convexity issues compared to the dual convex formulation
Information Theory for Trustworthy Machine Learning · Harvard · PhD
Tried and failed
greedy coordinate selection in coordinate descent applied to nonconvex optimization over manifolds. Outcome: too slow. Reason: per-iteration coordinate selection overhead outweighs the higher objective progress per step compared to cyclic or randomized rules
Large-Scale Optimization Methods: Theory and Applications · MIT · PhD
Tried and failed
direct accelerated gradient without proximal convexification applied to nonconvex composite optimization. Outcome: too slow. Reason: yields sub-optimal iteration complexity and requires bounded domain diameters
Accelerated Inexact First-Order Methods for Solving Nonconvex Composite Optimization Problems · Georgia Tech · PhD
Tried and failed
ellipsoid method for convex optimization applied to computing mixed strategies from marginal allocations. Outcome: too slow. Reason: practically inefficient and high computational overhead despite theoretical polynomial-time complexity
Strategic resource coordination for detecting illegal activity · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected cardinality-constrained convex optimization techniques (e.g., basis pursuit/L0 methods) for random feature coreset construction due to prohibitive computational expense in the large-data regime.
Practical Methods for Scalable Bayesian and Causal Inference with Provable Quality Guarantees · MIT · PhD
Convex relaxations produce large optimality gaps and fail to guarantee exactness
Relaxing non-convex constraints, binary terms, or network physics through semidefinite, linear, or continuous relaxations frequently yields loose bounds and non-physical variable assignments. In multiple instances, these relaxations fail to discover optimal trade-offs, suffer from non-zero duality gaps, or invalidate theoretical guarantees like truthfulness.
Tried and failed
Convex relaxation models applied to Optimal power flow with non-loss-minimizing objectives. Reason: Relaxations yielded large optimality gaps when objectives misaligned with physical loss minimization
MICROGRID ENERGY MANAGEMENT SYSTEM WITH ANCILLARY SERVICES TO THE GRID · Georgia Tech · PhD
Tried and failed
exact convex relaxation using branch flow models applied to bidirectional power flexibility optimization. Reason: bidirectional reserves violate the objective function monotonicity with respect to grid losses needed for exactness
Tried and failed
convex relaxation of non-convex quadratic programming applied to optimal power flow problems. Reason: the convex relaxation was too weak, yielding excessively large optimality gaps up to 93%
Autonomous optimal Power Flow via Convex Solution - Sequential Linear Programming · Georgia Tech · PhD
Tried and failed
Lagrangian duality for infinite-dimensional mediation programs applied to belief-based mechanism design optimization. Reason: Duality gap remains non-zero due to non-convexities in the belief-based mediation constraints.
Essays on the Economics of Information · MIT · PhD
Tried and failed
Linear programming relaxation of mixed-integer program applied to PDE-constrained network flow optimization. Reason: Relaxation produced non-tight bounds yielding non-physical flow and density decision variable values
On traffic state estimation and control in the world of connected vehicles · UT Austin · PhD
Considered and rejected
Considered and rejected: Rejected evaluating REIG_true directly due to non-concavity and infinite-dimensional search over the ambiguity set, adopting an affine tangent relaxation solvable via 1D convex duality
Efficient and Scalable Machine Learning Methods for Robust Bayesian Optimal Experimental Design · Georgia Tech · PhD
Tried and failed
rational sum-of-squares convex relaxation applied to polynomial neural network training. Reason: Denominator constraints to ensure feasibility either broke problem convexity or became unenforceable in optimization.
Theoretical and Computational aspects of Polynomial Neural Networks: Training Stability, Algorithmic Complexity and Expressivity · Harvard · Master's
Tried and failed
convex relaxation followed by sequential linear programming applied to volt/var power flow optimization. Outcome: worse than baseline. Reason: the convex relaxation fails to find the minimal objective value, acting only as a poor initialization
Autonomous optimal Power Flow via Convex Solution - Sequential Linear Programming · Georgia Tech · PhD
Tried and failed
convex hull constraints in semidefinite relaxation applied to discrete phase optimization. Reason: linear convex hull constraints provide negligible performance gains over standard relaxation for multi-bit resolutions
Advancing RIS Optimization: From Ideal to Realistic Models · Virginia Tech · Doctorate
Tried and failed
Lagrangian relaxation for multiobjective optimization applied to deterministic information bottleneck optimization. Reason: Lagrangian relaxation cannot discover solutions lying inside the non-convex regions of the Pareto frontier
Towards reliable organisms: fault-tolerance in unconventional models of computation · MIT · PhD
Tried and failed
convex hull relaxation of function classes applied to non-convex statistical learning. Outcome: worse than baseline. Reason: takes polynomial entropy numbers to exponential covering complexity, yielding suboptimal convergence rates
Essays on Algorithmic Learning and Uncertainty Quantification · MIT · PhD
Tried and failed
multiparametric disaggregation for non-convex bilinear terms applied to single-ratio fractional optimization. Outcome: worse than baseline. Reason: ineffective relaxation tightness and excessive computational overhead for linearizing fractional redistricting objectives
Embeddings for Disjunctive Programs with Applications to Political Districting and Rectangle Packing · Virginia Tech · Doctorate
Considered and rejected
Considered and rejected: Directly solving for A and B in inverse control dynamics by squared error loss containing high powers of A was rejected due to a non-convex, ill-conditioned optimization landscape, leading to a convex relaxation.
Learning Representations With Linear-Algebraic Structure · Duke · PhD
Considered and rejected
Considered and rejected: Replacing f+(z) with the multi-linear extension F(z) in the continuous convex relaxation of RSW, because it fails to upper-bound the optimal reward even asymptotically.
Online decision-making and learning under structured non-stationarity · UT Austin · PhD
Considered and rejected
Considered and rejected: Rejected continuous convex relaxations of discrete solvers because they induce suboptimal approximation ratio lower bounds.
Structured, Constrained and Creative Learning · Tübingen · PhD
Considered and rejected
Considered and rejected: Rejected convex relaxation and approximation methods for the VCG winner determination problem because non-convexity/sub-optimality invalidates the truthfulness guarantee.
Auction-Based Mechanisms for Power Grid Balancing using Cloud Datacenters · Carleton University · PhD
Tried and failed
standard linear relaxation proximity bounding applied to n-fold integer programming. Reason: L-infinity proximity between LP vertices and integer optima scales as Omega(n), precluding dimension-independent bounds
Results on Sparse Integer Programming and Geometric Independent Sets · EPFL · PhD
Tried and failed
lift-and-project convex relaxation with Benders decomposition applied to two-stage distributionally robust optimization. Outcome: too slow. Reason: slow convergence and stalling on large instances leading to computational timeout
Decomposition Methods in Column Generation and Data-Driven Stochastic Optimization · Georgia Tech · PhD
Mathematical programming formulations are outperformed by simpler baselines and specialized heuristics
Complex mathematical programming reformulations, regularized risk minimizers, and coordinate selection strategies frequently run slower or produce worse objective values than greedy heuristics and simple baselines. In several evaluations, dedicated solvers, cutting-plane methods, or standard gradient approaches solved faster and avoided convergence to poor local optima.
Tried and failed
linear programming for constrained dynamic ranking applied to fair dynamic learning to rank. Outcome: infeasible cost. Reason: High computational complexity from quadratic variables without providing better utility or fairness than simple proportional control
Fairness of Exposure for Ranking Systems · Cornell · PhD
Lost to a baseline
Under binary treatments, proposed general linear programming approach is more conservative or computationally expensive than Fogarty and Small (2016) and Rosenbaum (2018) specialized methods.
SENSITIVITY ANALYSIS METHODS FOR OBSERVATIONAL STUDIES WITH A CONTINUOUS EXPOSURE · Penn · PhD
Tried and failed
unconstrained neural network surrogate loss learning applied to decision-focused portfolio optimization. Outcome: worse than baseline. Reason: unconstrained non-convex surrogate loss functions lead to poor optimization and worse decision quality than standard two-stage baselines
Decision-Focused Learning for the Masses With Applications to Public Health · Harvard · PhD
Tried and failed
regularized empirical risk minimization applied to stochastic convex optimization. Outcome: worse than baseline. Reason: sample-independent regularization suffers constant suboptimality where stochastic gradient descent converges at optimal rates
Non-convex and Interactive Learning via Stochastic Optimization · Cornell · PhD
Tried and failed
hinge-loss bisection and alternating minimization applied to chance-constrained optimization with non-convex constraints. Outcome: worse than baseline. Reason: non-convexity in the decision set causes alternating minimization and convex approximations to miss feasible solutions
Chance Constrained Programs and Distributionally Favorable Optimization · Georgia Tech · PhD
Lost to a baseline
The reformulation solver underperformed the cutting-plane solver on the nonlinear non-convex pooling problem with an ellipsoidal uncertainty set (318 ms median vs 628 ms median).
Formulations, algorithms and software for robust optimisation · Imperial · PhD
Lost to a baseline
SOC relaxation had shorter convex solve runtime than the proposed AQCF convexification method in 4 out of 6 test cases
Autonomous optimal Power Flow via Convex Solution - Sequential Linear Programming · Georgia Tech · PhD
Tried and failed
constraint programming for combinatorial optimization applied to large-scale grid asset planning. Outcome: worse than baseline. Reason: Failed to reach optimality within time limit compared to mixed-integer programming.
Advanced Techno-Economic and Sustainability Analysis Methods of Emerging Grid Technologies · Georgia Tech · PhD
Lost to a baseline
IPOPT applied directly to 0-fairness (throughput) was beaten by GLOP linear programming solving the 0-1 multi-knapsack formulation due to convergence to poor local optima.
Joint Modeling and Performance Evaluation of Communication and Memory Systems in the Classical and the Quantum Internet: A Time-to-Live Approach · Leibniz Universität Hannover · PhD
Lost to a baseline
Integer Programming (IP) in Phase II SPP performed worse than or equal to Linear Programming (LP) across final cost, time steps taken, and computational run time for both Ship A and Ship B.
ONLINE OPTIMIZATION FOR ROUTING IN DYNAMIC CONTESTED ENVIRONMENTS · Naval Postgraduate School · Master's
Lost to a baseline
Linear programming Method #2 solved 10x slower (18 ms/point vs 1.8 ms/point for Method #1) when verifying feasible secure grasp spaces
The Design Of A Community-Informed Socially Interactive Humanoid Robot And End-Effectors For Novel Edge-Rolling · Penn · PhD
Tried and failed
ergodic iterate averaging in primal-dual methods applied to detecting infeasibility in convex optimization. Outcome: worse than baseline. Reason: averaging retains early iterates far from the infimal displacement vector, slowing down convergence
Complexity, conditioning, and saddle avoidance in nonsmooth optimization · Cornell · PhD
Tried and failed
unrolled projected gradient descent with surrogate objective applied to approximating constrained convex optimization. Outcome: worse than baseline. Reason: traditional gradient descent achieves better convergence accuracy at higher iteration counts
Aligning Machine Learning and Robust Decision-Making · MIT · PhD
Lost to a baseline
Our direct data-driven method has higher computational complexity than linearly parameterized baseline methods due to the inherent cost of moment-based convex relaxation.
Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach · Politecnico di Torino · PhD
Lost to a baseline
Runtime of the proposed minimax optimal convex regression estimator is n^O(d), which is significantly slower than the O_d(n^2) runtime of standard Least Squares.
On The Performance Of The Maximum Likelihood Over Large Models · MIT · PhD
High computational latency prevents mathematical programs and dynamic programming from meeting real-time requirements
Embedded platforms and onboard systems fail to execute quadratic, semidefinite, or dynamic programming solvers within the strict millisecond update rates required for real-time control. As a result, exact projection operators, nonlinear model predictive control, and dynamic programming recursions are consistently rejected due to prohibitive runtime and memory footprints.
Tried and failed
Quadratic programming for control barrier functions applied to multi-agent collision avoidance. Outcome: infeasible cost. Reason: Quadratic program solving exceeded computation time and memory constraints at scale.
Symmetries infused safe and scalable multi-robot policies · Penn · PhD
Tried and failed
online semidefinite programming for affine feedback policies applied to stochastic model predictive motion control. Outcome: too slow. Reason: Computational complexity exceeded embedded onboard hardware capacity to meet real-time control frequency requirements
Safe, High-performance Motion Planning Under Uncertainty for Autonomous Driving Applications · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected nonlinear model predictive control (NMPC) because online solving of non-convex nonlinear programming problems is computationally prohibitive and cannot guarantee global minima.
Data driven modeling and MPC Based control for Pathological Tremors · Virginia Tech · Master's
Considered and rejected
Considered and rejected: Rejected solving the pessimistic control problem via robust optimization/semidefinite programming because computing projection operators and SDPs was too computationally expensive for real-time rates compared to the idealistic control formulation.
Learning for autonomy in the wild : theory, algorithms, and practice · UT Austin · PhD
Considered and rejected
Considered and rejected: Rejected Dynamic Programming for high-fidelity parallel HEV supervisory control due to intractable computational burden of forward-facing models.
Energy management of hybrid and battery electric vehicles · Imperial · PhD
Considered and rejected
Considered and rejected: Rejected directly solving stochastic MPC with mixed parametric and process uncertainties due to severe computational intractability in non-linear dynamic programming.
Bayesian Learning: Paving the Way to Trustworthy Robots · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Computing the exact least-squares projection onto {c : ||Dc||_infty <= T} via quadratic programming at each iteration: rejected due to high computational expense
Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks · EPFL · PhD
Considered and rejected
Considered and rejected: Rejected using linear programming solvers to project/correct outputs online due to excessive computational overhead and poor scalability to larger neural networks.
Learning-directed systems with safety and robustness certificates · UT Austin · PhD
Lost to a baseline
Greedy HDA guidance runs within 2 seconds, whereas the reachability-steering HDA guidance algorithm requires 3 to 15 seconds to solve the non-convex optimization problem.
Hazard Detection and Avoidance for Autonomous Spacecraft Landing · Georgia Tech · PhD
Considered and rejected
Considered and rejected: Rejected bounding neural network Lipschitz constants via Mixed-Integer Programming or convex optimization for real-time applications due to excessive computational intensity.
On the theory of Lipschitz continuous machine learning · Oxford · PhD
Considered and rejected
Considered and rejected: Dynamic programming was rejected for flight routing due to high computational expense in real-time execution.
Data-Driven Approach using Machine Learning for Real-Time Flight Path Optimization · Georgia Tech · PhD
Numerical instability and conflicting constraints lead to algorithm divergence and solver infeasibility
Overlapping safety boundaries, active constraint configurations, and trigonometric terms frequently trigger solver infeasibility, division by zero, or persistent oscillations. Furthermore, standard splitting and projected gradient schemes diverge or stall when applied across non-convex loss surfaces and non-smooth domains.
Tried and failed
strict quadratic programming with dual constraint functions applied to constrained safe control systems. Reason: conflict between stabilizing and safety constraint sets with bounded inputs causes optimization infeasibility
Learning, planning, and control for agile and safe robotic systems · UT Austin · PhD
Tried and failed
control barrier function quadratic programming applied to autonomous vehicle trajectory tracking under constraints. Outcome: did not converge. Reason: overlapping boundary constraints caused the optimization quadratic program to become infeasible
Barrier Functions For Safe Shared Autonomy · Georgia Tech · PhD
Tried and failed
differentiable quadratic programming solver layers applied to high-dimensional constrained optimal control. Outcome: unstable. Reason: numerical instability and implementation bugs when handling high-dimensional systems with many active constraints
Scalable and Safe Deep Learning Architectures for Stochastic Optimal Control Using Forward-Backward Stochastic Differential Equations · Georgia Tech · PhD
Tried and failed
sequential convex programming and off-the-shelf QCQP solvers applied to large parametric Markov decision processes. Outcome: did not converge. Reason: conservative step sizing and numerical instability caused timeouts on large models
Convex optimization meets formal methods : verification, synthesis, and learning in Markov decision processes · UT Austin · PhD
Considered and rejected
Considered and rejected: Mixed-Integer Nonlinear Programming (MINLP) formulation, rejected due to extreme computational complexity and difficulty finding feasible starting points.
Tried and failed
vanilla two-block ADMM applied to distributed AC optimal power flow. Outcome: did not converge. Reason: exhibited persistent oscillations across various penalty parameter settings due to nonconvexity
Decomposition algorithms based on the nonconvex augmented Lagrangian framework · Georgia Tech · PhD
Tried and failed
primal-dual splitting with adaptive step sizes applied to non-convex phase retrieval. Outcome: did not converge. Reason: algorithm fundamentally diverges in non-convex settings regardless of stepsize initialization
Scalable constrained optimization · EPFL · PhD
Tried and failed
evaluating convergence via subgradient norms or objective gap applied to nonsmooth nonconvex optimization. Reason: subgradient distance to zero remains strictly bounded away from zero even near optimal points
Some Extensions on the Reach of First-Order Optimization Theory · Cornell · PhD
Tried and failed
mixed-integer nonlinear programming applied to transient stability optimization in power converters. Outcome: did not converge. Reason: numerical instability and division by zero caused by unbounded trigonometric tangent terms in constraints
Modeling and enhancing transient stability of grid-forming converters · Imperial · PhD
Tried and failed
gradient descent optimizers with line search applied to constrained non-convex probability distribution optimization. Outcome: did not converge. Reason: optimizers failed to respect probability validity constraints during non-convex optimization
Principled Approaches for Latency Reduction in Networking Systems · MIT · PhD
Considered and rejected
Considered and rejected: Rejected over-complete independent component analysis (OICA) for proxy-based causal effect estimation due to non-convex optimization landscape and getting stuck in bad local minima.
On the identifiability and estimation of causal effects · EPFL · PhD
Considered and rejected
Considered and rejected: Standard projected gradient descent onto positive differences after each step for convex profile training: rejected due to poor optimization performance on non-convex training losses
Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks · EPFL · PhD
Considered and rejected
Considered and rejected: Decided against standard gradient descent and proximal gradient descent for optimizing the non-smooth multi-convex objective functions in MDDM and MFBR due to slow convergence and inequality constraints, choosing ADMM with block coordinate descent instead.
On Modeling Dependency Dynamics of Sequential Data: Methods and Applications · Virginia Tech · Doctorate
Considered and rejected
Considered and rejected: Position-level projected gradient descent for constrained OT was rejected because evaluating projections over general non-convex feasible sets is computationally intractable.
Routing Optimization for Transport and Sustainability · Tübingen · PhD
Left open by the authors
Problems the authors named and did not get to.
Left open
Establish explicit complementary slackness bounds for optimal dual variables in non-convex parametric settings to prove full PACC learnability. Blocker: Requires advanced mathematical proof and theoretical optimization expertise rather than software engineering.
LEARNING WITH POINTWISE CONSTRAINTS · Penn · PhD
Left open
Derive stability proofs for the explicit hybrid model predictive control law formulated via penalized trust region sequential convex programming. Blocker: None
Convex Optimization in a Nonconvex World: Applications for Aerospace Systems · University of Washington · PhD
Left open
Incorporate semidefinite programming convex relaxations of AC power flow into the grid resilience models to bound objective values and quantify suboptimality. Blocker: None
Threat and decision models for informing power grid resilience under uncertainty · UT Austin · PhD
Left open
Derive necessary and sufficient theoretical conditions for rank-1 exactness in the unbalance-constrained semidefinite programming optimal power flow formulation. Blocker: None
Voltage Unbalance-Cognizant Optimization of Distribution Grids · Virginia Tech · Master's
Left open
Incorporate sensitivity-informed neural network training into convex relaxations of AC optimal power flow problems. Blocker: None
Optimization, Learning, and Control for Energy Networks · Virginia Tech · Doctorate
Left open
Develop semidefinite programming and neural network approaches to identify effective energy functions for lossy power systems. Blocker: None
Inference, estimation, and prediction for stable operation of modern electric power systems · MIT · PhD
Left open
Formulate interior-point non-convex optimal power flow in eigen-basis coordinates and evaluate solver computational performance. Blocker: None
Real-time control and reconfiguration in eigen-basis coordinates for multi-phase unbalanced distribution networks · Imperial · PhD
Left open
Formulate and evaluate SOCP and SDP convex relaxations for OPF and Volt/Var Control in eigen-basis coordinates on distribution networks. Blocker: None
Real-time control and reconfiguration in eigen-basis coordinates for multi-phase unbalanced distribution networks · Imperial · PhD
Left open
Relax strictly-convex and concave assumptions in SSDS theoretical convergence analysis for non-convex loss functions and uncertainties. Blocker: None
Robust and scalable deep learning for cyber-physical systems · Iowa State · PhD
Left open
Extend the two-step convex optimization algorithm to hybrid AC/DC microgrids incorporating non-ideal converter dynamics with parasitic resistances. Blocker: None
Networked DC microgrids control system for optimal power exchange with guaranteed stability · Imperial · PhD
Who has worked on this
Authors of the public theses cited on this page, most-cited first.
- Jacob Knaup · Georgia Tech · PhD · 2024
Safe, High-performance Motion Planning Under Uncertainty for Autonomous Driving Applications - Gad Monga Ilunga · Georgia Tech · PhD · 2022
Autonomous optimal Power Flow via Convex Solution - Sequential Linear Programming - Abduljalil Aljadani · Imperial · PhD · 2025
Real-time control and reconfiguration in eigen-basis coordinates for multi-phase unbalanced distribution networks - Xuanliang Deng · Virginia Tech · Doctorate · 2025
Priority Assignment Algorithms for Real-Time Systems - Pakshal Narendra Bohra · EPFL · PhD · 2024
Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks - Ayush Sekhari · Cornell · PhD · 2022
Non-convex and Interactive Learning via Stochastic Optimization - Johannes Wiebe · Imperial · PhD · 2021
Formulations, algorithms and software for robust optimisation - Javad Ansarifar · Iowa State · Master's · 2021
Integer linear programming formulation for the unified duplication-loss-coalescence model - Karim Elsayed · Leibniz Universität Hannover · PhD · 2026
Joint Modeling and Performance Evaluation of Communication and Memory Systems in the Classical and the Quantum Internet: A Time-to-Live Approach - Nikolaos Bousias · Penn · PhD · 2026
Symmetries infused safe and scalable multi-robot policies - Ignacio Hounie · Penn · PhD · 2026
LEARNING WITH POINTWISE CONSTRAINTS - Yiming Chen · Georgia Tech · PhD · 2025
Advanced Techno-Economic and Sustainability Analysis Methods of Emerging Grid Technologies
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