## A Review of Trust Region Algorithms for Optimization

Citations: | 4 - 0 self |

### BibTeX

@MISC{Yuan_areview,

author = {Ya-Xiang Yuan},

title = {A Review of Trust Region Algorithms for Optimization},

year = {}

}

### OpenURL

### Abstract

Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper we give a review on trust region algorithms for nonlinear optimization. Trust region methods are robust, and can be applied to ill-conditioned problems. A model trust region algorithm is presented to demonstrate the trust region approaches. Various trust region subproblems and their properties are presented. Convergence properties of trust region algorithms are given. Techniques such as backtracking, non-monotone and second order correction are also briefly discussed. 1 Introduction Nonlinear optimization problems have the form min x2! n f(x) (1.1) s: t: c i (x) = 0; i = 1; 2; : : : ; m e ; (1.2) c i (x) 0; i = m e + 1; : : : ; m; (1.3) where f(x) and c i (x) (i = 1; : : : ; m) are real functions defined in ! n , at least one of these functions is nonlinear, and m m e are two non-negative integers. If m = m e = 0, problem (1.1) is an unconstrain...