OPT-Engine shows pure-text chain-of-thought reasoning in LLMs loses robustness as optimization complexity grows, external tools fix only local arithmetic, and solver-integrated methods are bottlenecked by automated constraint formulation.
arXiv preprint arXiv:2208.14314 (2022)
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DSPDHG extends PDHG and SPDHG with doubly stochastic block updates and proves O(1/K) ergodic convergence for the expected restricted primal-dual gap plus linear convergence for a restarted variant under quadratic growth.
A feasibility-pump-style alternating heuristic with dynamic convexification and parallel local branching finds feasible solutions for three previously unsolved QPLIB instances and improves best-known solutions for fifteen others within five minutes.
A filter line search SQP algorithm reduces iterations and computation time for nonconvex SOS programs compared to prior methods.
D-PDLP is the first distributed multi-GPU framework for PDLP that uses 2D grid partitioning of the constraint matrix plus nonzero-aware and random-permutation strategies to scale PDHG iterations with low overhead and full FP64 accuracy.
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OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling
OPT-Engine shows pure-text chain-of-thought reasoning in LLMs loses robustness as optimization complexity grows, external tools fix only local arithmetic, and solver-integrated methods are bottlenecked by automated constraint formulation.
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On the convergence of doubly stochastic Primal-Dual Hybrid Gradient Method
DSPDHG extends PDHG and SPDHG with doubly stochastic block updates and proves O(1/K) ergodic convergence for the expected restricted primal-dual gap plus linear convergence for a restarted variant under quadratic growth.
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An Alternating Primal Heuristic for Nonconvex MIQCQP with Dynamic Convexification and Parallel Local Branching
A feasibility-pump-style alternating heuristic with dynamic convexification and parallel local branching finds feasible solutions for three previously unsolved QPLIB instances and improves best-known solutions for fifteen others within five minutes.
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On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems
A filter line search SQP algorithm reduces iterations and computation time for nonconvex SOS programs compared to prior methods.
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D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems
D-PDLP is the first distributed multi-GPU framework for PDLP that uses 2D grid partitioning of the constraint matrix plus nonzero-aware and random-permutation strategies to scale PDHG iterations with low overhead and full FP64 accuracy.