A Cutting-plane and Benders' Decomposition Algorithm for Two-Stage Distributionally Robust Convex programs
Abstract
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex programs using cutting planes, with applications to solving distributionally-robust two-stage stochastic mixed-integer convex programs. Analysis is also given for the case where convex programming oracle provides an -optimal solution. We combine the cut generation with a branch-and-union scheme to develop a more practical algorithm. Computational results on generated test problems show the practicality of our algorithm. Specifically, results show that in the tested problems our algorithm achieves < 5% optimality gap in 12 hours. This gap is >17% with a commercial solver.
Cite
@article{arxiv.2112.04160,
title = {A Cutting-plane and Benders' Decomposition Algorithm for Two-Stage Distributionally Robust Convex programs},
author = {Fengqiao Luo and Shibshankar Dey and Sanjay Mehrotra},
journal= {arXiv preprint arXiv:2112.04160},
year = {2025}
}