Decomposition in conic optimization with partially separable structure
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.
Cite
@article{arxiv.1306.0057,
title = {Decomposition in conic optimization with partially separable structure},
author = {Yifan Sun and Martin S. Andersen and Lieven Vandenberghe},
journal= {arXiv preprint arXiv:1306.0057},
year = {2013}
}