On the convergence of a new trust region algorithm

Summary. In this paper we present a new trust region algorithm for general nonlinear constrained optimization problems. The algorithm is based on the exact penalty function. Under very mild conditions, global convergence results for the algorithm are given. Local convergence properties are also studied. It is shown that the penalty parameter generated by the algorithm will be eventually not less than the norm of the Lagrange multipliers at the accumulation point. It is proved that the method is equivalent to the sequential quadratic programming method for all large , hence superlinearly convergent results of the SQP method can be applied. Numerical results are also reported. Received March 21, 1993