A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint

TL;DR

This paper introduces an efficient conjugate gradient-based algorithm for large-scale nonconvex quadratic programming with a single quadratic constraint, leveraging sparsity and eigenvalue analysis to improve solution speed.

Contribution

The paper presents a novel conjugate gradient algorithm tailored for large-scale nonconvex QCQP with one quadratic constraint, exploiting sparsity and eigenvalues for efficiency.

Findings

The proposed method effectively solves large-scale QCQP problems.

Numerical experiments demonstrate the algorithm's competitiveness with recent methods.

The approach exploits sparsity and eigenvalue structure for computational efficiency.

Abstract

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the sparsity of the involved matrices and solves the problem via solving a sequence of positive definite system of linear equations after identifying suitable generalized eigenvalues. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with some recent algorithms in the literature.