A nonmonotone trust-region algorithm with nonmonotone penalty parameters for constrained optimization

In this paper, we present a nonmonotone trust-region algorithm with nonmonotone penalty parameters for the solution of optimization problems, with nonlinear equality constraints and bound constraints. The proposed algorithm combines an SQP approach with a trust-region strategy to globalize the process. Each step is obtained through the computation of a normal step (to reduce infeasibility) and a tangential step (to decrease some merit function). The algorithm makes use of an augmented Lagrangian function as merit function, and allows the value of this merit function and the penalty parameter involved in it to decrease nonmonotonically. The global convergence theory for the proposed algorithm is developed without regularity assumption, and shows that any limit point of the sequence generated by the algorithm is a ϕ-stationary point, while at least one limit point, under the suitable assumptions, is a substationary point (and a stationary point if it is feasible). Some preliminary numerical experiments are also reported.