Solving convex QPs with structured sparsity under indicator conditions

TL;DR

This paper investigates convex quadratic programming problems with structured sparsity controlled by binary indicators, proposing polynomial-time approximation algorithms and analyzing their complexity.

Contribution

It introduces a family of polynomial-time approximation algorithms for structured sparse convex QPs with indicator conditions, along with negative complexity results.

Findings

Algorithms achieve polynomial-time approximation for complex structured sparsity problems.

Certain problem classes are proven to be computationally hard.

The framework applies to various important quadratic optimization scenarios.

Abstract

We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a way that both the objective and the constraints are separable convex quadratics. We describe a family of polynomial-time approximation algorithms and negative complexity results.