Submodularity in Conic Quadratic Mixed 0-1 Optimization

• 成果类型: Article
• 署名作者: Atamturk, Alper; Gomez, Andres
• 署名单位: University of California System; University of California Berkeley; University of Southern California
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1888
• 发表日期: 2020
• 页码: 609-630
• 关键词: chvatal-gomory closure; service system-design; programming approach; convex relaxations; 2nd-order cone; algorithm; discrete; RISK; cuts; reformulations

摘要

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint over binary variables and unbounded continuous variables. We then generalize and strengthen the inequalities by incorporating additional constraints of the optimization problem. Computational experiments on mean-risk optimization with correlations, assortment optimization, and robust conic quadratic optimization indicate that the new inequalities strengthen the convex relaxations substantially and lead to significant performance improvements.