A Trust Region Method with Regularized Barzilai-Borwein Step-Size for Large-Scale Unconstrained Optimization

TL;DR

This paper introduces an advanced trust region optimization method that adaptively uses a regularized Barzilai-Borwein step-size combined with non-monotone techniques, improving efficiency for large-scale unconstrained problems.

Contribution

It presents a novel trust region method integrating a regularized Barzilai-Borwein step-size and non-monotone techniques, with proven convergence and practical efficiency.

Findings

Method effectively adapts step-size within trust regions.

Convergence of the algorithm is theoretically guaranteed.

Numerical experiments demonstrate improved performance.

Abstract

We develop a Trust Region method with Regularized Barzilai-Borwein step-size obtained in a previous paper for solving large-scale unconstrained optimization problems. Simultaneously, the non-monotone technique is combined to formulate an efficient trust region method. The proposed method adaptively generates a suitable step-size within the trust region. The minimizer of the resulted model can be easily determined, and at the same time, the convergence of the algorithm is also maintained. Numerical results are presented to support the theoretical results.