Practical proximal primal-dual algorithms for structured saddle point problems Practical proximal primal-dual algorithms for structured saddle point problems

In this paper, we are concerned with a class of convex-concave saddle point problems, where one of the objective parts is assumed to be a convex and smooth function with Lipschitz continuous gradient. By exploiting the bilinear structure of the objective, we first propose a practical accelerated Pro...

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Vydáno v:Journal of global optimization Ročník 93; číslo 3; s. 803 - 831
Hlavní autoři: Qu, Yunfei, He, Hongjin, Zhang, Tao, Han, Deren
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2025
Springer Nature B.V
Témata:
Algorithms
Computer Science
Convex analysis
Euclidean space
Lipschitz condition
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Saddle points
restarting technique
Primary 65K05
saddle point problem
inexact criterion
Primal-dual algorithm
90C25
65K10
accelerated algorithm
ISSN:0925-5001, 1573-2916
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Shrnutí:In this paper, we are concerned with a class of convex-concave saddle point problems, where one of the objective parts is assumed to be a convex and smooth function with Lipschitz continuous gradient. By exploiting the bilinear structure of the objective, we first propose a practical accelerated Proximal Primal-Dual algorithm (PPD+), which possesses an O ( 1 / N 2 ) convergence rate measured by the residual between two successive iterates, where N represents the iteration counter. In some cases, considering that the underlying subproblems of PPD+ cannot be easily solved exactly or up to a high precision, we further propose two inexact versions of the PPD+ under absolute and relative error criteria. Finally, we employ a restarting technique to enhance our algorithms for the purpose of making them more robust and efficient. A series of numerical experiments demonstrate that our algorithms perform well in practice.
Bibliografie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-025-01545-x