Linearly Convergent First-Order Algorithms for Semi-definite Programming
Optimization and Control
2013-09-10 v1
Abstract
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent algorithms for solving these formulations. Moreover, we introduce a bundle-level method which converges linearly uniformly for both smooth and non-smooth problems and does not require any smoothness information. The convergence properties of these algorithms are also discussed. Finally, we consider a special case of LMIs, linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a weaker assumption.
Cite
@article{arxiv.1309.2251,
title = {Linearly Convergent First-Order Algorithms for Semi-definite Programming},
author = {Cong D. Dang and Guanghui Lan},
journal= {arXiv preprint arXiv:1309.2251},
year = {2013}
}