A trust region algorithm for equality constrained optimization (Q1174456)

An iterative technique for solving equality constrained nonlinear optimization problems is considered. In each step a search direction from an approximate solution is calculated by solving a quadratic programming subproblem which approximates the original problem. In an earlier paper [ibid. 35, No. 3, 265--278 (1986; Zbl 0598.90079)] the authors proposed an algorithm in which the step-length of each iteration is determined by means of a differentiable exact penalty function. The present paper extends the results to the case where convergence is forced by means of trust regions instead of line searches. Basically, in each iteration a trial step (bounded by a positive parameter) in the search direction is subjected to tests before being accepted. Global convergence properties and a local superlinear convergence result are proved.