A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators
Optimization and Control
2021-10-26 v1
Abstract
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix defining the quadratic term in the objective is sparse. We use a graphical representation of the support of , and show that if this graph is a path, then we can solve the associated problem in polynomial time. This enables us to construct a compact extended formulation for the closure of the convex hull of the epigraph of the mixed-integer convex problem. Furthermore, we propose a novel decomposition method for general (sparse) , which leverages the efficient algorithm for the path case. Our computational experiments demonstrate the effectiveness of the proposed method compared to state-of-the-art mixed-integer optimization solvers.
Cite
@article{arxiv.2110.12547,
title = {A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators},
author = {Peijing Liu and Salar Fattahi and Andrés Gómez and Simge Küçükyavuz},
journal= {arXiv preprint arXiv:2110.12547},
year = {2021}
}