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

Caihua Chen; Xiaoling Fu; Bingsheng He; Xiaoming Yuan

doi:10.1007/s10957-016-1051-6

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

Caihua Chen, Xiaoling Fu, Bingsheng He, Xiaoming Yuan^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

Abstract

Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. 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.

Original language	English
Pages (from-to)	914-928
Number of pages	15
Journal	Journal of Optimization Theory and Applications
Volume	172
Issue number	3
DOIs	https://doi.org/10.1007/s10957-016-1051-6
Publication status	Published - 1 Mar 2017

Scopus Subject Areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

User-Defined Keywords

Convergence rate
Iteration complexity
Linear variational inequality
Projection methods

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10.1007/s10957-016-1051-6

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abstract = "Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. 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 = "Convergence rate, Iteration complexity, Linear variational inequality, Projection methods",

author = "Caihua Chen and Xiaoling Fu and Bingsheng He and Xiaoming Yuan",

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AU - Chen, Caihua

AU - Fu, Xiaoling

AU - He, Bingsheng

AU - Yuan, Xiaoming

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. 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.

AB - Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. 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.

KW - Convergence rate

KW - Iteration complexity

KW - Linear variational inequality

KW - Projection methods

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DO - 10.1007/s10957-016-1051-6

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ER -

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

Abstract

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