2 x 2-Convexifications for convex quadratic optimization with indicator variables

• 成果类型: Article
• 署名作者: Han, Shaoning; Gomez, Andres; Atamturk, Alper
• 署名单位: University of Southern California; University of California System; University of California Berkeley
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01924-w
• 发表日期: 2023
• 页码: 95-134
• 关键词: perspective reformulations; constraints; PROGRAMS; cardinality; relaxation; cuts

摘要

In this paper, we study the convex quadratic optimization problem with indicator variables. For the 2 x 2 case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the 2 x 2 case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including the optimal perspective relaxation and the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems.