We present a $.73$-approximation algorithm for a disjoint $2$-Catalog Segmentation and $.63$-approximation algorithm for the joint version of the problem. Previously best known results are $.65$ and $.56$, respectively. The results are based on semidefinite programming and a subtle rounding method. Citation Working Paper, Department of Management Sciences, Henry, B. Tippie College of Business, The … Read more
The convex feasibility problem asks to find a point in the intersection of finitely many closed convex sets in Euclidean space. This problem is of fundamental importance in mathematics and physical sciences, and it can be solved algorithmically by the classical method of cyclic projections. In this paper, the case where one of the constraints … 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
We present large-scale optimization techniques to model the energy function that underlies the folding process of proteins. Linear Programming is used to identify parameters in the energy function model, the objective being that the model predict the structure of known proteins correctly. Such trained functions can then be used either for {\em ab-initio} prediction or … 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
The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and … 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. Citation … 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
In this paper we introduce a conic optimization formulation for inequality-constrained convex programming, and propose a self-dual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively. Hence they are completely symmetric. This allows for … Read more
We formulate a block-iterative algorithmic scheme for the solution of systems of linear inequalities and/or equations and analyze its convergence. This study provides as special cases proofs of convergence of (i) the recently proposed Component Averaging (CAV) method of Censor, Gordon and Gordon ({\it Parallel Computing}, 27:777–808, 2001), (ii) the recently proposed Block-Iterative CAV (BICAV) … Read more