SOSTOOLS is a free MATLAB toolbox for formulating and solving sum of squares (SOS) optimization programs. It uses a simple notation and a flexible and intuitive high-level user interface to specify the SOS programs. Currently these are solved using SeDuMi, a well-known semidefinite programming solver, while SOSTOOLS handles internally all the necessary reformulations and data … Read more
We build upon the work of Fukuda et al.\ \cite{FuKoMuNa01} and Nakata et al.\ \cite{NaFuFuKoMu01}, in which the theory of partial positive semidefinite matrices has been applied to the semidefinite programming (SDP) problem as a technique for exploiting sparsity in the data. In contrast to their work, which improves an existing algorithm that is based … Read more
We introduce a computer program PENNON for the solution of problems of convex Nonlinear and Semidefinite Programming (NLP-SDP). The algorithm used in PENNON is a generalized version of the Augmented Lagrangian method, originally introduced by Ben-Tal and Zibulevsky for convex NLP problems. We present generalization of this algorithm to convex NLP-SDP problems, as implemented in … Read more
We show that SDP (semidefinite programming) and SOCP (second order cone programming) relaxations provide exact optimal solutions for a class of nonconvex quadratic optimization problems. It is a generalization of the results by S.~Zhang for a subclass of quadratic maximization problems that have nonnegative off-diagonal coefficient matrices of objective quadratic functions and diagonal coefficient matrices … Read more
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