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2000•SIAM Journal on OptimizationRequires access

Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization

Steven J. Benson, Yinyu Ye, Xiong Zhang

Open publisher page 281 citations

Abstract

We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large-scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational results of interior-point algorithms for approximating maximum cut semidefinite programs with dimension up to 3,000.

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What this paper is about

We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large-scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational results of interior-point algorithms for approximating maximum cut semidefinite programs with dimension up to 3,000.

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OpenAlex reports 281 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large-scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational results of interior-point algorithms for approximating maximum cut semidefinite programs with dimension up to 3,000.

Key concepts: Interior point method, Semidefinite programming, Mathematics, Quadratically constrained quadratic program, Scaling, Semidefinite embedding, Mathematical optimization, Dimension (graph theory)

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