Two globally convergent nonmonotone trust-region methods for unconstrained optimization

TL;DR

This paper introduces two new nonmonotone trust-region methods for unconstrained optimization, demonstrating their global convergence and superior performance through numerical experiments on standard test problems.

Contribution

The paper proposes two novel nonmonotone strategies integrated into trust-region methods, with proven convergence properties and improved efficiency over existing approaches.

Findings

Proven global convergence to stationary points.

Achieved local superlinear and quadratic convergence rates.

Numerical results show superior performance on benchmark problems.

Abstract

This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is motivated, then two new nonmonotone terms are proposed, and their combinations into the traditional trust-region framework are studied. The global convergence to first- and second-order stationary points and local superlinear and quadratic convergence rates for both algorithms are established. Numerical experiments on the \textsf{CUTEst} test collection of unconstrained problems and some highly nonlinear test functions are reported, where a comparison among state-of-the-art nonmonotone trust-region methods show the efficiency of the proposed nonmonotne schemes.