# A new nonmonotone adaptive trust region algorithm

## TL;DR

This paper introduces a novel nonmonotone adaptive trust region algorithm for unconstrained optimization, featuring a radius-dependent shrinkage parameter and a new strategy to enhance convergence and robustness.

## Contribution

It presents a new algorithm with innovative radius adjustment and nonmonotone strategies, improving convergence and robustness over existing methods.

## Key findings

- Demonstrates efficiency on CUTEst benchmark problems
- Shows robustness across various unconstrained optimization tasks
- Achieves favorable convergence properties

## Abstract

In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and it exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from the CUTEst package.