Uncertain standard quadratic optimization under distributional assumptions: a chance-constrained epigraphic approach

TL;DR

This paper explores a chance-constrained epigraphic approach to address the NP-hard standard quadratic optimization problem under uncertain data matrices, with applications in portfolio optimization, clustering, and dynamics.

Contribution

It introduces a novel chance-constrained framework for uncertain StQP with known data distribution, extending existing models to indefinite cases.

Findings

The approach effectively handles uncertainty in non-convex quadratic problems.

It demonstrates improved solution robustness under data distribution assumptions.

The method is applicable to real-world problems like portfolio and clustering optimization.

Abstract

The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life applications ranging portfolio optimization to pairwise clustering and replicator dynamics. Sometimes, the data matrix is uncertain. We investigate models where the distribution of the data matrix is known but where both the StQP after realization of the data matrix and the here-and-now problem are indefinite. We test the performance of a chance-constrained epigraphic StQP to the uncertain StQP.