Document Type : Original Article

Authors

• Seyed Hamzeh Mirzaei ¹
• Ali Ashrafi ²

¹ Department of Mathematics, ُ Semnan University

² عضو هیات علمی

Abstract

Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonocity condition will decrease the convergence speed of this method. Therefore, improving and increasing the efficiency of this method is one of the most important issues and the attention of researchers.

Methodology: Establishing a new adaptive trust region radius as well as combining the trust region method with a non-monotone strategy to avoid the adverse effects of monotonocity.

Findings: A new adaptive trust region radius converged to zero is provided and then trust region combination is performed with a non-monotone strategy. Running the algorithm on a set of test functions shows that the new adaptive radius along with the non-monotone strategy used significantly improves the efficiency of the trust region method.

Originality/Value: The presented non-monotone adaptive algorithm has a second-order convergence rate. In addition, it significantly reduces computational costs compared to traditional algorithms. On the other hand, the new adaptive radius avoids the ineffectiveness of the trust region close to the solution.

Keywords

• Unconstrained Optimization&lrm؛
• &lrm؛ Trust Region&lrm؛ Non-monotone Strategy&lrm؛
• &lrm؛ Global Convergence

Main Subjects

• Non-linear Optimization