# A new alternating direction trust region method based on conic model for solving unconstrained optimization

## TL;DR

This paper introduces a novel alternating direction trust region method based on a conic model for unconstrained optimization, improving solvability and efficiency, especially for large-scale problems.

## Contribution

It proposes a new conic model trust region subproblem solved via an alternating direction approach, overcoming previous difficulties and establishing global convergence.

## Key findings

- Outperforms the dogleg method in numerical experiments
- Effective for large-scale unconstrained optimization problems
- Demonstrates better solvability of the subproblem

## Abstract

In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction method, the new conic model trust region subproblem is solved by two steps in two orthogonal directions. This new idea overcomes the shortcomings of conic model subproblem which is difficult to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that this method may be better than the dogleg method to solve the subproblem, especially for large-scale problems.