ConstOptBench: Evaluating LLMs on Verifiable Constrained Optimization Reasoning without Tool Use

Existing Large Language Models (LLMs) optimization benchmarks primarily evaluate whether models can formulate problems for external solvers, leaving direct reasoning about feasibility and optimality largely unmeasured. We introduce ConstOptBench, a solver-verified benchmark for evaluating tool-free constrained optimization reasoning. It contains 400 programmatically generated convex problems spanning linear programming, quadratic programming, quadratically constrained quadratic programming, and geometric programming, with four controlled levels of structural difficulty. Given explicit objectives and constraints, models must output the optimal objective value without using external tools. Across five proprietary and open-weight models, GPT-5.5 achieves the highest overall accuracy at 97.2% and shows the smallest decline as difficulty increases; several other LLMs exhibit a large accuracy drop. Accuracy is consistently highest on linear programs, while performance on the other problem classes varies substantially across models. Diagnostic analysis attributes most failures to continued refinement beyond a correct intermediate solution, incomplete optimization reasoning, and partial constraint handling, whereas arithmetic errors are rare. These results also show that success on small constrained optimization problems does not necessarily translate into robust reasoning as variables and constraints increase.