An Improved Analysis of Semidefinite Approximation Bound for Nonconvex Nonhomogeneous Quadratic Optimization with Ellipsoid Constraints

TL;DR

This paper presents an improved analysis of semidefinite programming bounds for nonconvex quadratic optimization with ellipsoid constraints, enhancing previous results and providing tighter approximation ratios for specific cases.

Contribution

The paper introduces a novel analysis method that significantly improves existing SDP approximation bounds for ECQP, especially for assignment-polytope constrained problems.

Findings

Improved approximation bounds for special cases of ECQP.

Enhanced analysis technique surpassing Tseng's previous results.

Tighter approximation ratios for assignment-polytope constrained quadratic programs.

Abstract

We consider the problem of approximating nonconvex quadratic optimization with ellipsoid constraints (ECQP). We show some SDP-based approximation bounds for special cases of (ECQP) can be improved by trivially applying the extened Pataki's procedure. The main result of this paper is to give a new analysis on approximating (ECQP) by the SDP relaxation, which greatly improves Tseng's result [SIAM Journal Optimization, 14, 268-283, 2003]. As an application, we strictly improve the approximation ratio for the assignment-polytope constrained quadratic program.