A multiplier active-set trust-region algorithm for solving constrained optimization problem

Abstract

A new trust-region algorithm for solving a constrained optimization problem is introduced. In this algorithm, an active set strategy is used together with multiplier method to convert the computation of the trial step to easy trust-region subproblem similar to this for the unconstrained case. A convergence theory for this algorithm is presented. Under reasonable assumptions, it is shown that the algorithm is globally convergent. In particular, it is shown that, in the limit, a subsequence of the iteration sequence satisfies one of four types of stationary conditions. Namely, the infeasible Mayer–Bliss conditions, Fritz John’s conditions, the infeasible Fritz John’s conditions or KKT conditions.Preliminary numerical experiment on the algorithm is presented. The performance of the algorithm is reported. The numerical results show that our approach is of value and merit further investigation.