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arXiv · 1306.0057

Decomposition in conic optimization with partially separable structure

Yifan Sun·Martin S. Andersen·Lieven Vandenberghe
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Abstract

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower-dimensional cones. The most important example is sparse semidefinite programming with a chordal sparsity pattern. Here partial separability derives from the clique decomposition theorems that characterize positive semidefinite and positive-semidefinite-completable matrices with chordal sparsity patterns. The paper describes a decomposition method that exploits partial separability in conic linear optimization. The method is based on Spingarn's method for equality constrained convex optimization, combined with a fast interior-point method for evaluating proximal operators.

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Yifan Sun, Martin S. Andersen, Lieven Vandenberghe. 2013-06-01. Decomposition in conic optimization with partially separable structure. https://arxiv.org/abs/1306.0057

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