## A New Trust Region Algorithm For Equality Constrained Optimization (1995)

Citations: | 51 - 7 self |

### BibTeX

@MISC{Coleman95anew,

author = {Thomas F. Coleman and Wei Yuan},

title = {A New Trust Region Algorithm For Equality Constrained Optimization},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We present a new trust region algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level sets. The algorithm employs L 2 penalty functions for obtaining global convergence. Under certain assumptions we prove that this algorithm globally converges to a point satisfying the second order necessary optimality conditions; the local convergence rate is quadratic. Results of preliminary numerical experiments are presented. 1. Introduction. We consider the equality constrained optimization problem minimize f(x) subject to c(x) = 0 (1:1) where x 2 ! n and f : ! n ! !, and c : ! n ! ! m are smooth nonlinear functions. Problem (1.1) is often solved by successive quadratic programming (SQP) methods. At a current point x k 2 ! n , SQP methods determine a search direction d k by solving a quadratic programming problem minimize rf(x k ) T d + 1 2 ...