On Choosing Parameters in Retrospective-Approximation Algorithms for Simulation-Optimization

The simulation-optimization (SO) problem is a constrained optimization problem where the objective function is observed with error, usually through an oracle such as a simulation. Retrospective approximation (RA) is a general technique that can be used to solve SO problems. In RA, the solution to the SO problem is approached using solutions to a sequence of approximate problems, each of which is generated using a specified sample size and solved to a specified error tolerance. In this paper, our focus is parameter choice in RA algorithms, where the term parameter is broadly interpreted. Specifically, we present (i) conditions that guarantee convergence of estimated solutions to the true solution; (ii) convergence properties of the sample-size and error-tolerance sequences that ensure that the sequence of estimated solutions converge to the true solution in an optimal fashion; and (iii) a numerical procedure that efficiently solves the generated approximate problems for one-dimensional SO