In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In … Read more
The goal of this paper is to address the problem of evaluating the performance of a system running under unknown values for its stochastic parameters. A new approach called LAD for Simulation, based on simulation and classification software, is presented. It uses a number of simulations with very few replications and records the mean value … Read more
In this paper we discuss the issue of solving stochastic optimization problems by means of sample average approximations. Our focus is on rates of convergence of estimators of optimal solutions and optimal values with respect to the sample size. This is a well-studied problem in case the samples are independent and identically distributed (i.e., when … Read more
We consider an optimization problem of minimization of a linear function subject to chance constraints. In the multidimensional case this problem is, generically, a problem of minimizing under a nonconvex and difficult to compute constraints and as such is computationally intractable. We investigate the potential of conceptually simple scenario approximation of the chance constraints. The … Read more
Response surface methods show promising results for global optimization of costly non convex objective functions, i.e. the problem of finding the global minimum when there are several local minima and each function value takes considerable CPU time to compute. Such problems often arise in industrial and financial applications, where a function value could be a … Read more
We present a simulation-based analytic center cutting plane method to solve a sample average approximation of a call center problem of minimizing staffing costs, while maintaining an acceptable level of service in multiple time periods. We establish convergence of the method when the service level functions are discrete pseudoconcave. An extensive numerical study of a … Read more
In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form $\max\{u(y):y=(y^1,\ldots,y^n)\in\setY^1\times\cdots\times\setY^n\}$, i.e., in which the feasible region is a Cartesian product … Read more