Constrained Search via Penalization for Continuous Simulation Optimization

This article presents a constrained search via penalization (CSP) framework for solving continuous simulation optimization problems involving stochastic constraints. Rather than addressing feasibility separately, CSP utilizes a penalty function method to convert the original problem into a series of simulation optimization problems without stochastic constraints that are then solved via adaptive search. We present conditions under which the CSP approach converges almost surely from inside the feasible region, and under which it converges to the optimal solution but without feasibility guarantee. We also conduct numerical studies aimed at assessing the efficiency of CSP under the two different convergence modes. Our numerical results show that the CSP method converges to the optimal solution in all settings we considered. Moreover, it converges faster when the optimal solution is interior to the feasible region. Finally, if there are binding constraints at the optimal solution, then convergence is faster when feasibility is not guaranteed.