Approximate first-order primal-dual algorithms for the saddle point problems

2020 ◽  
pp. 1
Author(s):  
Fan Jiang ◽  
Xingju Cai ◽  
Zhongming Wu ◽  
Deren Han
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
First Order ◽  
Primal Dual

scholarly journals Accelerated Stochastic Algorithms for Convex-Concave Saddle-Point Problems

2021 ◽  
Author(s):  
Renbo Zhao
Keyword(s):  
Saddle Point ◽  
State Of The Art ◽  
Stochastic Algorithms ◽  
Stochastic Algorithm ◽  
Saddle Point Problems ◽  
First Order ◽  
Strongly Convex ◽  
Primal Dual ◽  
Oracle Complexity ◽  
Better Than

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this problem. When the gradient noises obey sub-Gaussian distributions, the oracle complexity of our restart scheme is strictly better than any of the existing methods, even in the deterministic case. Furthermore, for each problem parameter of interest, whenever the lower bound exists, the oracle complexity of our restart scheme is either optimal or nearly optimal (up to a log factor). The subroutine used in this scheme is itself a new stochastic algorithm developed for the problem where the saddle function is nonstrongly convex in the primal variable. This new algorithm, which is based on the primal-dual hybrid gradient framework, achieves the state-of-the-art oracle complexity and may be of independent interest.

scholarly journals Optimal Primal-Dual Methods for a Class of Saddle Point Problems

2014 ◽  
Vol 24 (4) ◽  
pp. 1779-1814 ◽  
Author(s):  
Yunmei Chen ◽  
Guanghui Lan ◽  
Yuyuan Ouyang
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
Dual Methods ◽  
Primal Dual

scholarly journals A Primal-Dual Algorithm with Line Search for General Convex-Concave Saddle Point Problems

2021 ◽  
Vol 31 (2) ◽  
pp. 1299-1329
Author(s):  
Erfan Yazdandoost Hamedani ◽  
Necdet Serhat Aybat
Keyword(s):  
Saddle Point ◽  
Line Search ◽  
Saddle Point Problems ◽  
Dual Algorithm ◽  
Primal Dual ◽  
General Convex
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