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

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• 作者：Caihua Chen ; Xiaoling Fu ; Bingsheng He…
• 关键词：Linear variational inequality ; Projection methods ; Convergence rate ; Iteration complexity
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：3
• 页码：914-928
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

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.