Peijing Liu – Optimization Online

Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators

Published: 2024/04/06

(Mixed) Integer Nonlinear Programming facets, indicator variables, Quadratic optimization, sparsity, supermodularity

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 … Read more

A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators

Published: 2021/10/21

(Mixed) Integer Nonlinear Programming, Statistics convex hull, decomposition, Fenchel dual, graphical models, indicator variables, Quadratic optimization, sparsity

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the objective is sparse. We use a graphical representation of the support of Q, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This … Read more