A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs

Samuel Burer (burermath.gatech.edu)
Renato Monteiro (monteiroisye.gatech.edu)
Yin Zhang (zhangcaam.rice.edu)

Abstract: The authors of this paper recently introduced a transformation \cite{BuMoZh99-1} that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based on the transformation, they proposed a globally convergent, first-order (i.e., gradient-based) log-barrier algorithm for solving a class of linear SDPs. In this paper, we discuss an efficient implementation of the proposed algorithm and report computational results on semidefinite relaxations of three types of combinatorial optimization problems. Our results demonstrate that the proposed algorithm is indeed capable of solving large-scale SDPs and is particularly effective for problems with a large number of constraints.

Keywords: semidefinite program, semidefinite relaxation, nonlinear programming, interior-point methods, limited memory quasi-Newton methods

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Combinatorial Optimization (Other )

Category 3: Nonlinear Optimization (Unconstrained Optimization )

Citation: School of ISyE, Georgia Tech, Atlanta, GA, USA, June 2001

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Entry Submitted: 06/03/2001
Entry Accepted: 06/04/2001
Entry Last Modified: 06/06/2001

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