Chapter Four · failure evidence
What Constrained Optimization got wrong, from 78 dissertations
Across various engineering and mathematical domains, constrained optimization formulations frequently encounter difficulties with solver infeasibility, over-conservative bounding, and numerical non-convexities. Practitioners also observe that imperfect constraint surrogates or omitted physical constraints lead to degraded objective performance, severe solution oscillations, or violations compared to simpler baselines. These records come from PhD theses at 22 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.
Overly conservative bounds and heavy constraint weights degrade optimization performance
Imposing overly strict constraint weights, conservative bounding approximations, or uniform risk allocations causes optimizers to trap in suboptimal local minima. These restrictive formulations reduce search efficiency and produce worse objective values than less constrained alternatives.
Tried and failed
diagonally dominant approximations for positive semidefiniteness applied to convex relaxations of polynomial optimization. Outcome: worse than baseline. Reason: diagonal dominance is overly conservative compared to exact semidefinite constraints, yielding substantially weaker bounds
Tried and failed
heavily weighted constraints in method of moving asymptotes applied to density-based topology optimization. Outcome: worse than baseline. Reason: overly strict constraint weights caused optimizer to get trapped in suboptimal local minima with poor performance
High-Efficiency Topology Optimization for Very Large-Scale Integrated-Photonics Inverse Design · Georgia Tech
Tried and failed
non-negative weight constraints applied to confounder balancing weights estimation. Outcome: worse than baseline. Reason: constraining weights to the simplex hurt empirical performance compared to unconstrained optimization
Adversarial Machine Learning Methods for Causal Inference under Unmeasured Confounding · Cornell
Tried and failed
Single-objective extreme weighting in multi-objective heuristic search applied to constrained spatial path finding. Outcome: worse than baseline. Reason: Extremes degrade search efficiency and Pareto trade-offs compared to balanced joint optimization.
Semantically diverse and spatially constrained queries · Iowa State
Tried and failed
regret-based Bayesian optimization acquisition function applied to privacy-constrained personalization querying. Outcome: worse than baseline. Reason: Failed to outperform uniform querying across privacy-constrained personalization simulations.
Essays on the Decision Value of Data in Marketing Measurement and Targeting · Penn
Tried and failed
multi-objective evolutionary optimization for single target priority applied to constrained resource allocation. Outcome: worse than baseline. Reason: Pareto compromise solutions underperform dedicated single-objective optimization when only one metric is prioritized
Integrating social equity into sustainable programming of road projects : a quantitative approach · UT Austin
Tried and failed
optimization-based block preconditioner tuning applied to stiff PDE system linear solvers. Outcome: worse than baseline. Reason: optimization over the affine subspace was overly constrained
Tried and failed
raw constraint sensitivity regularization without relevance filtering applied to chance-constrained trajectory optimization. Reason: over-constrains the problem and fails to generate conservative collision-avoidance trajectories
Games of Pursuit-Evasion with Multiple Agents and Subject to Uncertainties · Georgia Tech
Tried and failed
uniform risk allocation across constraints applied to chance-constrained trajectory optimization. Outcome: worse than baseline. Reason: leads to overly conservative trajectories and suboptimal final covariance ellipsoid volumes compared to optimized allocation
Model-Based and Data-Driven Covariance Control: Theory and Applications · Georgia Tech
Tried and failed
constrained optimal control with strict multi-derivative bounds applied to vehicle speed trajectory planning. Outcome: worse than baseline. Reason: strict acceleration and jerk bounds prevented overshooting, increasing total travel time compared to unconstrained trajectory
An Interdisciplinary and Probabilistic Treatment of Contemporary Highway Design Standards · Virginia Tech
Tried and failed
naive constraint conditions in constrained optimization applied to regularized neural network training. Outcome: worse than baseline. Reason: naive constraints caused over-regularization that harmed training performance
Lost to a baseline
Linear RTMPC and its learned policy achieved larger nominal tracking error than standard MPC when position constraints were tight, due to conservative tube-based constraint tightening.
Efficient Imitation Learning for Robust, Adaptive, Vision-based Agile Flight Under Uncertainty · MIT
Lost to a baseline
Bernstein/RBF positive semi-definite parameterizations exhibit slight accuracy degradation compared to Chebyshev polynomials due to increased conservativeness of stability constraints.
High-dimensional data driven parameterized macromodeling · IRIS - POLITO - prod
Tried and failed
distance-thresholded active learning exploration applied to chemical reaction optimization. Outcome: worse than baseline. Reason: Similarity constraints failed to outperform random sampling in small sample-size regimes
Tried and failed
small candidate pool size in batch Bayesian optimization applied to iterative molecular property optimization. Outcome: worse than baseline. Reason: overly constrained candidate pool degraded optimization performance compared to larger pool sizes
Molecular Property Predictors for Downstream De Novo Generation · Harvard
Considered and rejected
Considered and rejected: Rejected single-objective Bayesian optimization with rigid user constraints or fused metrics because it fails to capture high-dimensional resource trade-offs and substitutability.
Design and Management Strategies for Hardware Accelerators · DukeSpace
Considered and rejected
Considered and rejected: Rejected optimal control with artificial potentials for counter-swarming due to high constraints and prescribed trajectories that degrade swarm flexibility.
DEEP LEARNING METHODS FOR DECENTRALIZED DECISION-MAKING IN COUNTERSWARM ENGAGEMENTS · Calhoun
Strict and conflicting constraints cause optimization infeasibility and convergence failure
Optimization algorithms fail to converge when dynamic boundaries, geometric obstacles, or stochastic scenarios create infeasible constraint sets. Solvers struggle to identify feasible operating points without appropriate relaxations or dynamic feasibility initializations.
Tried and failed
equality-constrained nonsmooth Newton optimization applied to industrial cogeneration power targeting. Outcome: did not converge. Reason: equality formulation failed to converge across initial guesses, requiring inequality constraints
Tried and failed
multi-stage stochastic optimisation applied to sustainable energy asset planning. Outcome: did not converge. Reason: optimisation constraints could not be satisfied for a fraction of uncertainty scenarios
Risk-based methods for the valuation and planning of sustainable energy assets. · Cranfield
Tried and failed
restricted affine policy for chance-constrained optimization applied to stochastic power system dispatch. Outcome: did not converge. Reason: Restricted policy parameterization lacked expressiveness to satisfy chance constraints under high uncertainty variance.
Machine Learning and Quantum Computing for Optimization Problems in Power Systems · Virginia Tech
Tried and failed
sequential path stepping gradient descent optimization applied to constrained robotic trajectory planning. Outcome: did not converge. Reason: algorithm failed in environments with tight obstacles and long paths
Remote robotic manipulation task execution using affordance primitives · UT Austin
Tried and failed
tightening constraints directly in model predictive control applied to nonlinear trajectory tracking under uncertainty. Outcome: did not converge. Reason: direct constraint tightening caused severe optimization infeasibility compared to predictive reference generation
Learning-based Model Predictive Control for Aerial Vehicles · Penn
Tried and failed
sampling-based trajectory optimization with multimodal proposals applied to cluttered motion planning. Outcome: did not converge. Reason: failed to find feasible trajectories despite increasing sample counts and proposal covariances in constrained environments
Tried and failed
dynamic movement primitives under waypoint constraints applied to robot trajectory generation with obstacle avoidance. Outcome: did not converge. Reason: hyperparameters failed to reliably find trajectories satisfying both intermediate via-point and obstacle avoidance constraints
Automatically Encoding, Modifying, and Finding Robot Skills to Repair High-Level Tasks · Cornell
Tried and failed
direct transcription trajectory optimization via sequential quadratic programming applied to low-altitude orbit launch trajectory design. Reason: zenith angle geometric boundary constraints rendered low-altitude orbital targets mathematically infeasible
Optimal trajectories for a ground-to-orbit laser-propelled launch vehicle · Iowa State
Tried and failed
sequential quadratic programming without dynamic feasibility warm-start applied to constrained trajectory optimization. Outcome: did not converge. Reason: omitting initial dynamic feasibility checks caused consistent primal infeasibility during nonlinear optimization
Dynamic whole-body planning for humanoids in confined spaces : a morphology-aware synthesis approach · UT Austin
Tried and failed
single-variable boundary projection under stoichiometric constraints applied to chemical process efficiency target optimization. Reason: adjusting only one feed flow violated the minimum stoichiometric lower-bound constraints, causing mathematical infeasibility
Tried and failed
Standard Bayesian optimization and genetic algorithms applied to Constrained black-box optimization. Reason: Struggled to find feasible points or violated constraints without explicit mixed-integer programming integration.
Sequential black-box optimization via global optimization of tree ensembles · Imperial
Tried and failed
Gaussian process Bayesian optimization with weighted expected improvement applied to multi-objective circuit parameter optimization. Outcome: did not converge. Reason: trapped in local optima and failed to satisfy multiple stringent constrained specifications simultaneously
Efficient optimization methods for analog/mixed-signal integrated circuits via machine learning · UT Austin
Tried and failed
quadratic programming with strict physiological bound constraints applied to musculoskeletal inverse dynamics torque estimation. Outcome: did not converge. Reason: kinematic irregularities and non-smooth dynamics made strictly bounded constraints mathematically infeasible
Understanding motor control and impairment: An upper-limb model for muscular assessment · EPFL
Considered and rejected
Considered and rejected: Rejected hard obstacle constraints in Koopman MPC because model prediction inaccuracies cause infeasibility and deadlock near the constraint boundary.
Koopman Dynamic Modeling and Control for Robotic Systems Making and Breaking Contact · MIT
Flawed constraint encodings and heuristic surrogates lead to poor decisions and constraint violations
Relying on expectation based constraints, unconstrained surrogate losses, or decoupled greedy heuristics fails to guarantee feasibility and reduces decision quality. Decoupling constraints from gradient updates or enforcing safety filters only at test time produces severely suboptimal or invalid policies.
Tried and failed
expectation-based constraint formulations in constrained optimization applied to stochastic optimal power flow. Reason: optimizing average constraints permitted high-frequency individual limit violations across scenarios
Machine Learning and Quantum Computing for Optimization Problems in Power Systems · Virginia Tech
Tried and failed
two-stage stochastic optimization with fairness constraints applied to power grid resilience investment. Reason: Strict efficiency constraints cause non-monotonic worst-case risk reduction as investment budget increases
Decision-making under uncertainty in power systems and economics · UT Austin
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
relying solely on line search for constraint feasibility applied to constrained reinforcement learning policy optimization. Outcome: worse than baseline. Reason: omitting gradient-level constraint alignment provided insufficient correction compared to combining gradient optimization with line search
Risk-Aware Reinforcement Learning with Safety Constraints · MIT
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
Tried and failed
standard greedy heuristics for constrained optimization applied to constrained influence maximization on networks. Reason: Violated activation constraints yielding zero objective value or severely underperformed on target coverage
Spreading information in social networks containing adversarial users · Iowa State
Tried and failed
decoupled objective heuristics for constrained diffusion applied to influence maximization with competing constraints. Reason: heuristics either over-activated non-targets yielding zero value or activated too few targets
Constrained submodular optimization and applications in information diffusion · Iowa State
Considered and rejected
Considered and rejected: Rejected KKT-constrained gradient descent in favor of standard GD with projection/bounding onto [0,1] when the mixing matrix is overdetermined with independent columns
Linear Spectral Unmixing Algorithms for Abundance Fraction Estimation in Spectroscopy · YorkSpace
Considered and rejected
Considered and rejected: Rejected directly optimizing feature vectors followed by trajectory reconstruction in motion attribution because target feature vectors often have no physically realizable trajectory satisfying domain constraints.
Making Robot Behaviors Automatically Transparent · ResearchWorks
Considered and rejected
Considered and rejected: Rejected continuous/simultaneous optimization of robot motion and physical parameters in an alternating sequence (optimizing motion, then body parameters, then actuators successively) because parameter constraints lock the robot into suboptimal designs or infeasible states.
Co-Optimization and Co-Learning Methods for Automated Design of Rigid and Soft Robots · MIT
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: Rejected training an unconstrained deep FBSDE policy and augmenting a control barrier function safety filter at test-time, because it leads to sub-optimal policies compared to training in a constrained state-space.
Scalable and Safe Deep Learning Architectures for Stochastic Optimal Control Using Forward-Backward Stochastic Differential Equations · Georgia Tech
Non-convexities and numerical discontinuities disrupt solver stability and cause local trapping
Constraints introducing trigonometric terms, non-convex feasible sets, or numerical simulation tolerances disrupt gradient calculations and trap solvers in local optima. Furthermore, evaluating projections over complex non-convex constraints creates severe computational bottlenecks that prevent real time convergence.
Tried and failed
gradient-based optimization with numerical simulation constraints applied to thermodynamic cycle design optimization. Outcome: did not converge. Reason: numerical solver tolerances and cycle constraints disrupted gradient calculation and convergence
A Method for the Conceptual Design of Integrated Variable Cycle Engines and Aircraft Thermal Management Systems · Georgia Tech
Tried and failed
Nelder-Mead simplex optimization applied to constrained power dispatch optimization. Outcome: did not converge. Reason: Objective space discontinuities caused by high-persistence constraints trapped the solver in local minima
Economic, System, and Community-Based Optimization of Off-Grid Wave Energy Conversion · ResearchWorks
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 2-clothoid segment constrained optimization using fmincon because iterative numerical solvers cannot guarantee convergence in real-time execution
Autonomous Vehicle Waypoint Navigation Using Hyper-Clothoids · Virginia Tech
Considered and rejected
Considered and rejected: Rejected directly using physics-informed machine learning equations for contingency analysis because power flow equations lack closed forms and domain constraints arise dynamically.
Explainable and Network-based Approaches for Decision-making in Emergency Management · 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
Tried and failed
direct loss optimization with road constraints applied to trajectory forecasting models. Outcome: worse than baseline. Reason: hyperparameter sensitivity and convergence to local minima
A journey toward generalizable trajectory forecasting models · EPFL
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
Lost to a baseline
Looser fabrication constraints produced a poorer local optimum (68.8% vs >90% transmission) compared to tighter constraints due to non-convex optimization trapping
High-Efficiency Topology Optimization for Very Large-Scale Integrated-Photonics Inverse Design · Georgia Tech
Considered and rejected
Considered and rejected: Rejected convexification of unsafe obstacle regions for constrained trajectory optimization due to overly restrictive geometric assumptions.
Decision-Making Architectures for Control of Uncertain Systems · Georgia Tech
Considered and rejected
Considered and rejected: Rejected using explicit nonlinear flight-time constraints in NLP optimizers (e.g. SNOPT/IPOPT) due to unnecessary numerical optimization burden compared to explicit PST flight-time functions.
Spacecraft trajectory optimization using many embedded Lambert problems · UT Austin
Considered and rejected
Considered and rejected: Rejected Schur stability and Lyapunov matrix inequality (SDP) constraints for Koopman learning due to nonconvexity and computational intractability on large systems.
Constrained formulations are beaten or matched by unconstrained and simpler baselines
Unconstrained methods and simple heuristics frequently achieve lower costs, better tracking, or higher Sharpe ratios by violating constraints or avoiding optimization overhead. In addition, satisfying strict constraints often demands excessive computation time compared to fast unweighted baselines.
Lost to a baseline
On the IEEE 14-bus benchmark, reinforcement learning (RL) achieved a lower optimality gap deviation from MIPS (0.6%) than the proposed ICNN (1.53 ± 0.27%), albeit violating feasibility constraints.
Data-driven Methods for Optimal Power Flow in Smart Grids · YorkSpace
Lost to a baseline
Proposed MPC controller achieved higher cost (2.0545x10^4) than unconstrained optimal LQG (893.5569), though LQG violated the constraint (3.9272 > 2).
Lost to a baseline
Under the distortion constraint (d_hat = 0.2), Constrained Thompson Sampling was beaten in long-term average cost by Unconstrained Thompson Sampling in the coexistence scenario, and Constrained EXP3 was beaten in average cost by Unconstrained EXP3.
On the Value of Online Learning for Cognitive Radar Waveform Selection · Virginia Tech
Lost to a baseline
Constrained minimum-variance portfolio using RSVAR (0.087) had a statistically significantly lower Sharpe ratio than the naive rule (0.112) on Dataset 1.
Lost to a baseline
Trust-region algorithm and genetic algorithm for constrained optimization were matched or outperformed by a simpler two-stage coarse grid search
Modeling Healthcare Policy: From Calibration to Optimization · ResearchWorks
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
Lost to a baseline
Sensitivity-Driven Greedy Algorithm (3.95) satisfied OAR dose-volume constraints in the initial approximate solve where unweighted (P2) did not, but required ~2000s vs 2.8s
Optimization Formulations and Algorithms for Cancer Therapy · ResearchWorks
Lost to a baseline
Differential inverse kinematics achieved lower RMSE (0.0036m x, 0.0044m y, 0.00055m z) than gradient projection (0.0037m, 0.0034m, 0.0070m) and ANFIS (0.1309m, 0.0209m, 0.1261m), but failed joint limit constraints.
Development of Methodologies, Mechatronic Solutions and Controls for Upper Body Rehabilitative Robotics · IRIS - POLITO - prod
Omitting critical dynamic and physical constraints leads to instability and solution degeneracy
Failing to incorporate dynamic stability, contact measurements, or symmetry constraints leaves unconstrained degrees of freedom that destabilize system controllers. Without explicit physical constraints, models generate nonphysical distortions and cannot differentiate stable equilibria from unstable saddle points.
Tried and failed
semidefinite relaxation optimal power flow applied to networked DC microgrids control. Outcome: unstable. Reason: steady-state operating points lacked negative eigenvalues without explicit dynamic stability constraints
Networked DC microgrids control system for optimal power exchange with guaranteed stability · Imperial
Considered and rejected
Considered and rejected: Rejected augmented Lagrangian simultaneous (x, p) PDE optimization because force balance constraints alone cannot distinguish stable equilibria from unstable saddle points.
Computational Inverse Design of Shape Morphing Structures · EPFL
Tried and failed
unconstrained parameter regression without symmetry constraints applied to lattice parameter prediction from diffraction patterns. Outcome: overfit. Reason: optimizing unconstrained parameters achieved lower training loss through nonphysical distortions, degrading generalization performance
Enabling Autonomous high-throughput XRD-based Phase Discovery in Thin film systems · Cornell
Tried and failed
kinematic trajectory estimation without dynamic constraints applied to satellite orbit and gravity field determination. Reason: nominal and true trajectories could not be reconciled without joint dynamical parameter estimation
Tried and failed
nonlinear model predictive control without steady-state references applied to over-actuated trajectory tracking. Outcome: unstable. Reason: unconstrained state optimization caused solver convergence issues and severe control oscillations
Path tracking control of a multi-actuated autonomous vehicle at the limits of handling. · Cranfield
Tried and failed
kinematic-inertial estimation without contact constraints applied to legged robot state estimation. Outcome: unstable. Reason: omitting contact measurements leaves unconstrained degrees of freedom leading to solution degeneracy
Proprioceptive State Estimation for Legged Robots with Probabilistic and Hybrid Kinodynamics · Georgia Tech
Considered and rejected
Considered and rejected: Modeling robots as admittance (prescribed motions) in quasi-static models: rejected because output cannot be uniquely determined and violates non-penetration constraints in multi-contact grasps.
Left open by the authors
Problems the authors named and did not get to.
Left open
Optimize dynamic graph linkage addition and removal strategies for transactive energy peer-to-peer microgrid simulations with power flow constraints. Blocker: Lack of specified mathematical objective function and baseline simulation codebase
A Mycorrhizal Model for Transactive Energy Markets · Virginia Tech
Left open
Develop an optimization framework to synchronize multi-energy systems including hydrogen, gas, heating, and cooling networks with electrical grid flexibility needs. Blocker: Lacks specific mathematical formulations, constraints, network topologies, and performance benchmarks for the integrated multi-energy system
Left open
Develop a CoED graph neural network pipeline to predict AC-OPF solutions that strictly satisfy power grid physical constraints. Blocker: None
Developing Differentiable Toolkits for Computational Biology · Harvard
Left open
Develop power flow algorithms integrated with electricity market frameworks accounting for market prices, generation costs, and system constraints. Blocker: The unfinished work describes an extremely broad research direction (optimal power flow / market clearing) without a concrete formulation, objective, or target algorithm.
Power Flow Calculation of Power Systems with Renewable Penetration and AC/DC grids · Research Repository UCD
Left open
Optimize resource overhead for photonic graph state generation protocols under varying physical and circuit constraints. Blocker: Lacks specific target metrics, objective functions, or concrete constraint formulations
Controlling Quantum Systems for Computation and Communication · Virginia Tech
Left open
Theoretically analyze why 2-OPT-C yields significant query efficiency improvements over competing constrained Bayesian optimization methods. Blocker: None
Left open
Impose value function constraints on offline diverse skill extraction and evaluate discriminator-free successor feature objectives for near-optimal performance. Blocker: None
Structured, Constrained and Creative Learning · Publikationssystem UB Tuebingen
Left open
Benchmark the ML-based decomposition heuristic on highly-constrained electric vehicle routing problem benchmark instances with extra operational constraints. Blocker: None
Leveraging Machine Learning Methods to Solve Electric Vehicle Routing Problem Variants · Research Repository UCD
Left open
Derive performance bounds comparing receding-horizon regret-optimal control to infinite-horizon constrained regret-optimal policy using MPC proof techniques. Blocker: None
Optimal Control under Uncertainty: From Regret Minimization to Distributional Robustness · EPFL
Left open
Formulate and implement robust Omega ratio portfolio optimization models with explicit factor exposure constraints. Blocker: None
Essays on portfolio optimization and estimation risk · Research Repository UCD
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