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- Anton J. Kleywegt, Alexander Shapiro, Tito Homem-de-Mello
- SIAM Journal on Optimization
- 2002

In this paper we study a Monte Carlo simulation–based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is… (More)

- Tito Homem-de-Mello
- ACM Trans. Model. Comput. Simul.
- 2003

In this article we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study <i>variable-sample</i> techniques, in which the objective function is replaced, <i>at each iteration</i>, by a sample average approximation. We first provide general results on the <i>schedule</i> of sample sizes,… (More)

- Tito Homem-de-Mello, Sanjay Mehrotra
- SIAM Journal on Optimization
- 2009

In this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second-order stochastic dominance constraints. By using the polyhedral properties of this dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex… (More)

- Krishna Chepuri, Tito Homem-de-Mello
- Annals OR
- 2005

An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD) is considered. We propose a new heuristic method to solve the problem. The algorithm is a modified version of the so-called Cross-Entropy method, which has been proposed in the literature as a heuristics for deterministic combinatorial optimization problems… (More)

- Alexander Shapiro, Tito Homem-de-Mello
- SIAM Journal on Optimization
- 2000

In this paper we discuss Monte Carlo simulation based approximations of a stochastic programming problem. We show that if the corresponding random functions are convex piecewise linear and the distribution is discrete, then an optimal solution of the approximating problem provides an exact optimal solution of the true problem with probability one for… (More)

- Jian Hu, Tito Homem-de-Mello, Sanjay Mehrotra
- Math. Program.
- 2012

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems allows for the modeling of optimization problems where a riskaverse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with the case of multi-variate stochastic dominance under… (More)

- Tito Homem-de-Mello
- SIAM Journal on Optimization
- 2008

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… (More)

- Lijian Chen, Tito Homem-de-Mello
- Annals OR
- 2010

We study some mathematical programming formulations for the origin-destination model in airline revenue management. In particular, we focus on the traditional probabilistic model proposed in the literature. The approach we study consists of solving a sequence of two-stage stochastic programs with simple recourse, which can be viewed as an approximation to a… (More)

- Tito Homem-de-Mello
- INFORMS Journal on Computing
- 2007

W discuss the problem of estimating probabilities of rare events in static simulation models using the recently proposed cross-entropy method, which is a type of importance-sampling technique in which the new distributions are successively calculated by minimizing the cross-entropy with respect to the ideal (but unattainable) zero-variance distribution. In… (More)

In this paper we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variable-sample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general results on the schedule of sample sizes, under which… (More)