We propose a new relaxation scheme for the MAX-CUT problem using second-order cone programming. We construct relaxation problems to reflect the structure of the original graph. Numerical experiments show that our relaxation approaches give better bounds than those based on the spectral decomposition proposed by Kim and Kojima, and that the efficiency of the branch-and-bound … Read more
The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities … Read more
Adaptive Simulated Annealing (ASA) is a C-language code developed to statistically find the best global fit of a nonlinear constrained non-convex cost-function over a D-dimensional space. Citation%A L. Ingber %R Global optimization C-code %I Caltech Alumni Association %C Pasadena, CA %T Adaptive Simulated Annealing (ASA) %D 1993 %K 200701 %L Ingber:1993:CODE-ASA %O URL http://www.ingber.com/#ASA-CODEArticleDownload View … Read more
We develop a method for generating valid convex polynomial inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities. ArticleDownload View PDF