# Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators

arXiv: https://arxiv.org/abs/2404.04236 · HTML: https://mlsanity.com/paper/2404.04236/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators](https://mlsanity.com/paper/2608.01385/) (2026)

## Abstract (arXiv)

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.