Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider … Read more
In this paper, we prove that the Chvatal-Gomory closure of a set obtained as an intersection of a strictly convex body and a rational polyhedron is a polyhedron. Thus, we generalize a result of Schrijver which shows that the Chvatal-Gomory closure of a rational polyhedron is a polyhedron. ArticleDownload View PDF
Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address … Read more
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the … Read more
In this paper, we analyze two popular semidefinite programming \SDPb relaxations for quadratically constrained quadratic programs \QCQPb with matrix variables. These are based on \emph{vector-lifting} and on \emph{matrix lifting} and are of different size and expense. We prove, under mild assumptions, that these two relaxations provide equivalent bounds. Thus, our results provide a theoretical guideline … Read more
This paper presents and studies several models for multi-criterion budget allocation problems under uncertainty. We start by introducing a robust weighted objective model, which is developed further using the concept of stochastic dominance to incorporate risk averseness of the decision maker. A budget minimization variant of this model is also presented. We use a Sample … Read more
We present new insights into how to achieve higher frequencies in large-scale nonlinear predictive control using truncated-like schemes. The basic idea is that, instead of solving the full nonlinear programming (NLP) problem at each sampling time, we solve a single, truncated quadratic programming (QP) problem. We present conditions guaranteeing stability of the approximation error derived … Read more
Probabilistically constrained problems, in which the random variables are finitely distributed, are non-convex in general and hard to solve. The p-efficiency concept has been widely used to develop efficient methods to solve such problems. Those methods require the generation of p-efficient points (pLEPs) and use an enumeration scheme to identify pLEPs. In this paper, we … Read more
Airline revenue management is about identifying the maximum revenue seat allocation policies. Since a major loss in revenue results from cancellations and no-show passengers, over the years overbooking has received a significant attention in the literature. In this study, we propose new models for static and dynamic single-leg overbooking problems. In the static case, we … Read more
While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: \emph{When is the product of finitely many positive … Read more