We present a nontrivial family of facet-defining inequalities for the p-median polytope. We incorporate the inequalities in a branch-and-cut scheme, and we report computational results that demonstrate their effectiveness. CitationDepartment of Industrial Engineering, State University of New York at Buffalo, submittedArticleDownload View PDF
We present a family of inequalities that are valid for the generalized assignment polytope. Although the inequalities are not facet-defining in general, they define facets of a polytope of a relaxation. We report computational results on the use of the inequalities in a branch-and-cut scheme that demonstrate their effectiveness. CitationDepartment of Industrial Engineering, State University … Read more
We present a polyhedral study of the complementarity knapsack problem, in which no auxiliary binary variables are introduced, but rather the inequalities are derived in the space of the continuous variables. CitationSchool of Industrial and Systems Engineering, GA Tech, under reviewArticleDownload View PDF
The linear support vector machine can be posed as a quadratic program in a variety of ways. In this paper, we look at a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint when the Wolfe dual is taken. The quadratic term is … Read more
We define the concept of a computational grid, and describe recent work in solving large and complex optimization problems on this type of platform; in particular, integer programming, the quadratic assignment problem, and stochastic programming problems. This article focuses on work conducted in the metaneos project. CitationPreprint, Mathematics and Computer Science Division, Argonne National Laboratory. … Read more
The aim of this paper is to introduce cooperative games with a feasible coalition system which is an antimatroid. These combinatorial structures generalize the permission structures, which have nice economical applications. With this goal, we first characterize the approaches from a permission structure with special classes of antimatroids. Next, we use the concept of interior … Read more
In this paper we describe iNEOS, an Internet-based environment which facilitates the solution of complex nonlinear optimization problems. It enables a user to easily invoke a remote optimization code without having to supply the model to be optimized. An interactive communication between client and server is established and maintainted using CORBA. We test the system … Read more
GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More’ and Toraldo, this algorithm was designed for large-scale problems but had been implemented only for a single processor. The TAO implementation is available for a wide range of high-performance architecture, and has been … Read more
We describe version 2.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the LANCELOT, LOQO, MINOS, and SNOPT solvers on these problems. CitationTechnical Report ANL/MCS-246 Mathematics and Computer Science Division Argonne National Laboratory … Read more
The revised simplex method is often the method of choice when solving large scale sparse linear programming problems, particularly when a family of closely-related problems is to be solved. Each iteration of the revised simplex method requires the solution of two linear systems and a matrix vector product. For a significant number of practical problems … Read more