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arXiv · 1309.2251

Linearly Convergent First-Order Algorithms for Semi-definite Programming

Cong D. Dang·Guanghui Lan
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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.

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Cong D. Dang, Guanghui Lan. 2013-09-09. Linearly Convergent First-Order Algorithms for Semi-definite Programming. https://arxiv.org/abs/1309.2251

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