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arXiv · 1906.07013

First-order primal-dual algorithm with correction

Xiaokai Chang·Sanyang Liu
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Abstract

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which result in larger step sizes. The step sizes are predicted by using a local information of the linear operator and corrected by linesearch to satisfy a very weak condition, even weaker than the boundedness of sequence generated. The convergence and ergodic convergence rate are established for general cases, and in case when one of the prox-functions is strongly convex. The numerical experiments illustrate the improvements in efficiency from the larger step sizes and acceptable range of parameters.

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Xiaokai Chang, Sanyang Liu. 2019-06-17. First-order primal-dual algorithm with correction. https://arxiv.org/abs/1906.07013

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