Work

A cutting-plane and benders’ decomposition algorithm for two-stage distributionally robust convex programs

Year: 2025

Type: article

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 $$\epsilon -$$ ϵ - 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 $$<5\%$$ < 5 % optimality gap in 12 hours. This gap is $$>17\%$$ > 17 % with a commercial solver.

Source: Mathematical Programming

DOI: 10.1007/s10107-025-02288-z

Authors: Fengqiao Luo, Shibshankar Dey, Sanjay Mehrotra

Institution: Northwestern University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Office of Naval Research