A robust trust region method for nonlinear optimization with inequality constraint

A new trust region algorithm for inequality constrained optimization is presented, which solves two linear programming subproblems and a serious of quadratic subproblems at each successful iteration to obtain a acceptable trial step. The algorithm can circumvent the difficulties associated with the possible inconsistency of trust region subproblem. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even when the original problems itself is infeasible. Some global convergence properties are proved without regularity assumption and local superlinear convergence of the algorithm is obtained under standard conditions. Preliminary numerical results are reported on some classic problems.