Chapter Four · failure evidence
What Convex & Mathematical Programming got wrong, from 112 dissertations
The records document failures across convex optimization, mixed-integer programming, dynamic programming, and non-convex relaxation schemes. Common obstacles include exponential computational complexity on large instances, non-convex landscapes causing solver divergence or local minima, and loose relaxation bounds producing suboptimal or infeasible solutions. These records come from PhD theses at 21 institutions, 2021 to 2026. 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.
Mixed-integer and integer programming formulations suffer solver timeouts and intractable scaling on combinatorial problems
Exact integer linear and quadratic programming solvers frequently timed out or exhausted system memory on large graphs, scheduling tasks, and multi-agent coordination problems. Proving lower bounds and exploring exponential search spaces caused integer formulations to scale poorly and lose to greedy heuristics.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 · Calhoun
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
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
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
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 · Publikationssystem UB Tuebingen
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 · DukeSpace
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
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.
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
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
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
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
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
Non-convex optimization landscapes trigger solver divergence, local minima, and non-zero duality gaps
Non-convex constraints and non-concave objectives caused alternating minimization, gradient methods, and splitting algorithms to diverge or oscillate persistently. Formulations also suffered from non-zero duality gaps, frequent infeasibility, and entrapment in poor local optima.
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
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
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
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.
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
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
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
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
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.
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
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
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
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
Tried and failed
exact convex optimization applied to privacy metric optimization. Reason: problem convexity could not be established under general probability spaces
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
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
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
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
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 · DukeSpace
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
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
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
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
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
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 Repository
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
Iterative convex solvers and first-order methods experience high overhead and lag behind simpler baselines
Coordinate descent, projected gradient descent, and linear programming iterations incurred heavy computational overhead or sub-optimal convergence rates compared to standard baselines. Methods such as the ellipsoid method and unrolled projected gradient descent proved practically inefficient or failed to outperform analytical and heuristic approaches.
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
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
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
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
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
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
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
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
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 · JScholarship
Tried and failed
iterative dynamic piecewise linear approximation applied to separable concave quadratically constrained programming. Outcome: worse than baseline. Reason: insufficient iteration budget caused poorer objective values than global non-linear solvers
Piecewise Linear Approximation for Separable Concave Programming Problems · Texas Tech
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
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
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
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
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
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
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
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
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
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 · Publikationssystem UB Tuebingen
Convex relaxations produce loose bounds, large optimality gaps, or non-physical solutions
Relaxing non-convex or mixed-integer problems into semidefinite, second-order cone, or linear programs frequently yielded non-tight bounds and large optimality gaps up to 93 percent. In several settings, the relaxed solutions failed to satisfy original problem constraints, destroyed physical monotonicity, or invalidated game-theoretic truthfulness guarantees.
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
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
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
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.
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
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
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
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
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
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
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
Considered and rejected
Considered and rejected: Trace-norm convex relaxation of low-rank matrix recovery was rejected because solutions to the relaxed objective do not necessarily satisfy the original low-rank rank-constrained non-convex problem.
Safe and transferable multi-task bandit learning with shared representations and safe reinforcement learning · Iowa State
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 · Publikationssystem UB Tuebingen
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 Institutional Repository
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
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
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
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 · IRIS - POLITO - prod
Quadratic and semidefinite programming solvers exceed real-time computation budgets or face constraint infeasibility
Solving quadratic programs and semidefinite programs online exceeded embedded onboard compute capacity and memory limits in real-time control applications. Conflicting or overlapping safety and stabilization constraints additionally caused quadratic programs to become numerically unstable or infeasible.
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
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
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
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
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
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
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
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
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 · ResearchWorks
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
Considered and rejected
Considered and rejected: Rejected solving the exact quadratic program for norm amplification curves due to intractability; adopted a semi-definite programming (SDP) relaxation with Laplacian dual witnesses instead.
Towards Better Understanding of Algorithms and Complexity of Some Learning Problems · ResearchWorks
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
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
Dynamic programming and exact nonlinear models collapse under high-dimensional state spaces
Exact dynamic programming formulations suffered severe computational intractability when applied to forward-facing vehicle models, hybrid robotic state spaces, and fine wire segmentations. Authors rejected dynamic programming and massive nonlinear programming models in favor of heuristics and discretized approximations to avoid prohibitive memory and runtime costs.
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
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
Considered and rejected
Considered and rejected: Rejected using exact dynamic programming on hybrid state spaces for complex robotic motion planning due to prohibitive computational complexity.
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
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.
Considered and rejected
Considered and rejected: Rejected exact dynamic programming marginalization over all BPE segmentations due to intractable computational overhead
Building and Evaluating Open-Vocabulary Language Models · JScholarship
Considered and rejected
Considered and rejected: Rejected pure dynamic programming on finely divided wire segments due to prohibitive O(segment count) runtime and high memory usage.
Post-layout interconnect optimization algorithms · Iowa State
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
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.
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 · ResearchWorks
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
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
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
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
Left open
Formulate interior-point non-convex optimal power flow in eigen-basis coordinates and evaluate solver computational performance. Blocker: None
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
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
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
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