A direct search method for nonlinear programming

An iterative model algorithm Sbr minimizing a Lipschitz-continuous function subject to continuous constraints is introduced. Each iteration, of the me thod proceeds in two phases. In the first phase, feasibility is improved an d, as a result, a more feasible intermediate point is obtained. In the seco nd phase the algorithm tries to obtain a decrease of the objective function on an auxiliary feasible set. The output of the second phase is a trial po int that is compared with the current iterate by means of a suitable merit function. If the merit function is sufficiently decreased, the trial point is accepted. Otherwise, it is rejected and the second phase is repeated in a reduced domain. Global convergence results are proved and practical appli cations are commented.