Inexact restoration method for derivative-free optimization with smooth constraints (Q2848191)

Nonlinear programming problems, in which the derivatives of the objective function are not available, are approached with the condition of availability of the derivatives of the constraints. Highly nonlinear constraints are taken into account. A new method for solving this kind of problems is introduced based on the inexact restoration technique. It consists in two phases, in the case of smooth constrained optimization. The first phase, the restoration one, consists in improving feasibility. In the second phase, the optimization one, the goal is improving the objective function under constraints, which linearly approximate the initial ones. Since information on the derivatives of the objective function are either not known or expensive to evaluate, the second phase is based on derivative free methods. The convergence of the algorithm is studied. Finally, computer implementation details are discussed, also presenting numerical experiments.