DSDP4 is an implementation of the dual-scaling algorithm for semidefinite program ming. New features in this version include a Lanczos procedure for determining the step size, more precise primal solutions, a parallel solver, and improved performance on the standard test suites. CitationANL/MCS-TM-255; Mathematics and Computer Science Division; Argonne National Laboratory; Argonne, IL; March 2002ArticleDownload View … Read more
This paper demonstrates how interior-point methods can use multiple processors efficiently to solve large semidefinite programs that arise in VLSI design, control theory, and graph coloring. Previous implementations of these methods have been restricted to a single processor. By computing and solving the Schur complement matrix in parallel, multiple processors enable the faster solution of … Read more
GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality or integer constraints. It generates a series of lower bounds monotonically converging to the global optimum. Numerical experiments show that for most of … Read more
Recently,Tseng extended a class of merit functions for the nonlinear complementarity problem to semidefinite complementarity problem (SDCP), showing some properties under suitable assumptions. Yamashita and Fukushima also presented other properties. In this paper, we propose a new class of merit functions for the SDCP, and prove some of those properties, under weaker hypothesis. Particularly, we … Read more
Given a semi algebraic set S of R^n we provide a numerical approximation procedure that yields upper and lower bounds on mu(S), for measures mu that satisfy some given moment conditions. The bounds are obtained as solutions of positive semidefinite programs that can be solved via standard software packages like the LMI MATLAB toolbox. CitationAnnals … Read more
In this paper we present a primal-dual inexact infeasible interior-point algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and our analysis does not require feasibility to be maintained even if the initial iterate happened to be a … Read more
This article describes a generalization of the PBM method by Ben-Tal and Zibulevsky to convex semidefinite programming problems. The algorithm used is a generalized version of the Augmented Lagrangian method. We present details of this algorithm as implemented in a new code PENNON. The code can also solve second-order conic programming (SOCP) problems, as well … Read more
We study approximation bounds for the SDP relaxation of quadratically constrained quadratic optimization: min f^0(x) subject to f^k(x)
We consider the global minimization of a multivariate polynomial on a semi-algebraic set \Omega defined with polynomial inequalities. We then compare two hierarchies of relaxations, namely, LP-relaxations based on products of the original constraints, in the spirit of the RLT procedure of Sherali and Adams and recent SDP (semi definite programming) relaxations introduced by the … Read more
We consider the general nonlinear optimization problem in 0-1 variables and provide an explicit equivalent positive semidefinite program in $2^n-1$ variables. The optimal values of both problems are identical. From every optimal solution of the former one easily find an optimal solution of the latter and conversely, from every solution of the latter one may … Read more