A global convergence theory for an active-trust-region algorithm for solving the general nonlinear programing problem

Abstract

A new trust-region active-set algorithm for solving minimizing a nonlinear function subject to nonlinear equality and inequality constraints is described. In this algorithm, an active set strategy is used together with a projected Hessian technique to compute the trial step. A convergence theory for this algorithm is presented. Under important assumptions, it is shown that the algorithm is globally convergent. In particular, it is shown that a subsequence of the iteration sequence is not bounded away from either Fritz–John points or KKT points.