Efficient Algorithm for QCQP problem with Multiple Quadratic Constraints

TL;DR

This paper introduces a comprehensive global algorithm for solving QCQP problems with multiple quadratic constraints, combining cutting plane, spectral decomposition, and relaxation techniques, with proven convergence.

Contribution

It presents a novel, unified algorithm capable of efficiently solving complex QCQP problems with multiple quadratic constraints, extending applicability to general quadratic matrices.

Findings

Algorithm converges globally

Effective for multiple quadratic constraints

Applicable to general quadratic matrices

Abstract

Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the corresponding upper bound estimate is given by the SCO algorithm; then the corresponding lower bound convex relaxation is given by McCormick envelope. Based on this, we propose a global algorithm for this problem and establish the convergence of the algorithms. What's more, the algorithm is still valid for QCQP with multiple quadratic constraints and quadratic matrix in general form.