Polyhedral analysis of quadratic optimization problems with Stieltjes matrices and indicators

• 成果类型: Article; Early Access
• 署名作者: Liu, Peijing; Atamturk, Alper; Gomez, Andres; Kucukyavuz, Simge
• 署名单位: University of Southern California; University of California System; University of California Berkeley; Northwestern University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-025-02272-7
• 发表日期: 2025
• 关键词: Augmented Lagrangian method; perspective cuts

摘要

In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse graphical inference problems and others. We describe an explicit convex formulation for the problem by studying the Stieltjes polyhedron arising as part of an extended formulation and exploiting the supermodularity of a set function defined on its extreme points. Our computational results confirm that the proposed convex relaxation provides an exact optimal solution and may be an effective alternative, especially for instances with large integrality gaps that are challenging with the standard approaches.