Adaptive projected SOR algorithms for nonnegative quadratic programming

TL;DR

This paper introduces adaptive PSOR algorithms that automatically tune the relaxation parameter using Wolfe conditions, improving performance in nonnegative quadratic programming without extra assumptions.

Contribution

The paper proposes novel adaptive PSOR algorithms that dynamically control the relaxation parameter, enhancing efficiency and applicability in nonnegative quadratic programming.

Findings

Algorithms often outperform fixed-parameter PSOR.

Performance is comparable or superior to nearly optimal fixed parameters.

Method requires negligible additional computational cost.

Abstract

The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel adaptive PSOR algorithms that adaptively control the relaxation parameter using the Wolfe conditions. The method and its variants can be applied to various problems without requiring additional assumptions, barring the positive semidefiniteness concerning the matrix that defines the objective function, and the cost for updating the parameter is negligible in the whole iteration. Numerical experiments show that the proposed methods often perform comparably to (or sometimes superior to) the PSOR method with a nearly optimal relaxation parameter.