We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations: in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron–a problem that often arises in combinatorial optimization–has supermodular optimal costs. In addition, we examine the computational complexity of the least core … Read more
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
In this paper, simple linear programming procedure is proposed for generating all efficient extreme points and all efficient extreme rays of a multiple objective linear programming problem (V P). As an application we solve the linear multiplicative programming associated with the problem (VP). CitationsubmittedArticleDownload View PDF
This paper presents an outcome-space outer approximation algorithm for globally solving the linear multiplicative programming problem. We prove that the proposed algorithm is finite. To illustrate the new algorithm, we apply it to solve some sample problems. Citation10, Hanoi University of Technology, 07/2007ArticleDownload View PDF
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: 1. polynomial-time algorithms to exactly determine the number of Pareto optima and Pareto strategies; 2. a polynomial-space polynomial-delay prescribed-order enumeration algorithm … Read more
We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem. CitationWorking Paper, Tepper School of Business, Carnegie Mellon UniversityArticleDownload View PDF
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 study we consider a multiobjective integer linear stochastic programming problem with individual chance constraints. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. Some stability notions for such problem are characterized. An auxiliary problem is discussed and an algorithm as … Read more
In this paper we give the construction of the objective space of multiple objectives linear fractional programming (MOLFP) with equal denominators under the linear fractional mapping .In this case the decision space maps to an objective space of less dimension. The important of this study is that the decision-Maker may depend on extreme points of … Read more
In this paper a new method is suggested for solving the problem in which the objective function is a linear fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon solving this problem algebraically using the concept of duality. Since the earlier methods based … Read more