@Article{JCM-35-4,
author = {Dang, D., Cong and Lan, Guanghui and Zaiwen, Wen},
title = {Linearly Convergent First-Order Algorithms for Semidefinite Programming},
journal = {Journal of Computational Mathematics},
year = {2017},
volume = {35},
number = {4},
pages = {452--468},
abstract = {<p style="text-align: justify;">In this paper, we consider two different formulations (one is smooth and the other one is nonsmooth) for solving linear matrix inequalities (LMIs), an important class of semidefinite programming (SDP), under a certain Slater constraint qualification assumption. We then propose two first-order methods, one based on subgradient method and the other based on Nesterov&#39;s optimal method, and show that they converge linearly for solving these formulations. Moreover, we introduce an accelerated prox-level method which converges linearly uniformly for both smooth and non-smooth problems without requiring the input of any problem parameters. Finally, we consider a special case of LMIs, i.e., linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a much weaker assumption.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1612-m2016-0703},
url = {https://global-sci.com/article/84521/linearly-convergent-first-order-algorithms-for-semidefinite-programming}
}