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On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities

Caihua Chen(chchen***at***nju.edu.cn)
Xiaoling Fu(fuxlnju***at***hotmail.com)
Bingsheng He(hebma***at***nju.edu.cn)
Xiaoming Yuan(xmyuan***at***hkbu.edu.hk)

Abstract: Projection type methods are among the most important methods for solving monotone linear variational inequalities. In this note, we analyze the iteration complexity for two projection methods and accordingly establish their worst-case O(1/t) convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses, where t is the iteration counter. Our analysis does not require any error bound condition or the boundedness of the feasible set, and it is scalable to other methods of the same kind.

Keywords: Linear variational inequality, projection methods, convergence rate, iteration complexity

Category 1: Complementarity and Variational Inequalities

Citation:

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Entry Submitted: 01/13/2015
Entry Accepted: 01/13/2015
Entry Last Modified: 01/13/2015

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