Paper Info
Title
Complexity of Variants of Tseng's Modified F-B Splitting and Korpelevich's Methods for Hemivariational Inequalities with Applications to Saddle-point and Convex Optimization Problems
Abstract
In this paper, we consider both a variant of Tseng's modified forward-backward splitting method and an extension of Korpelevich's method for solving hemivariational inequalities with Lipschitz continuous operators. By showing that these methods are special cases of the hybrid proximal extragradient method introduced by Solodov and Svaiter, we derive iteration-complexity bounds for them to obtain different types of approximate solutions. In the context of saddle-point problems, we also derive complexity bounds for these methods to obtain another type of an approximate solution, namely, that of an approximate saddle point. Finally, we illustrate the usefulness of the above results by applying them to a large class of linearly constrained convex programming problems, including, for example, cone programming and problems whose objective functions converge to infinity as the boundaries of their effective domains are approached.
Year
DOI
Venue
2011
10.1137/100801652
SIAM Journal on Optimization
Keywords
Field
DocType
effective domain,derive complexity bound,modified forward-backward splitting method,lipschitz continuous operator,different type,convex programming problem,convex optimization problems,hemivariational inequalities,approximate solution,modified f-b splitting,hybrid proximal extragradient method,cone programming,approximate saddle point,complexity,convex optimization,saddle point
Saddle,Mathematical optimization,Saddle point,Infinity,Hemivariational inequality,Lipschitz continuity,Operator (computer programming),Convex optimization,Approximate solution,Mathematics
Journal
Volume
Issue
ISSN
21
4
1052-6234
Citations 
PageRank 
References 
27
1.39
5
Authors
2
Name
Order
Citations
PageRank
Renato D. C. Monteiro11250138.18
B. F. Svaiter260872.74