A Feasible Direction Method with Active-Set Identification for Derivative-Free Optimization

Abstract

We propose a model-based trust region method for derivative-free optimization with simulation-based inequality constraints. We are motivated by settings of simulation optimization in which both function evaluations at infeasible points may be unreliable and constraint evaluations are expensive. Our method maintains feasible incumbents and computes steps from a subproblem suitable for a feasible-direction method in order to encourage generation of feasible trial points. To reduce the computational cost of modeling the constraints, we describe an active-set estimation scheme that permits modeling with only a subset of constraints in each subproblem, as opposed to maintaining models of all constraints. We show that every limit point of the incumbents generated by our method is a Fritz-John point, and is additionally a KKT point under the Mangasarian-Fromovitz constraint qualification. Under standard nondegeneracy conditions, the active-set estimate identifies, within finite time, all constraints active at the limit point of the incumbents. Experiments on CUTEst problems show that our method generates feasible trial points far more often than a comparable SQP-based approach and solves more problems within a given budget with fewer function evaluations.