Outer-Inner Approximation Projection Methods for Multivalued Variational Inequalities

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• 作者：Pham Ngoc Anh ; Le Thi Hoai An
• 关键词：Multivalued variational inequalities ; Upper semicontinuous ; Linesearch ; Projection method
• 刊名：Acta Mathematica Vietnamica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：42
• 期：1
• 页码：61-79
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144
• 卷排序：42

文摘

In this paper, we present new projection methods for solving multivalued variational inequalities on a given nonlinear convex feasible domain. The first one is an extension of the extragradient method to multivalued variational inequalities under the asymptotic optimality condition, but it must satisfy certain Lipschitz continuity conditions. To avoid this requirement, we propose linesearch procedures commonly used in variational inequalities to obtain an approximation linesearch method for solving multivalued variational inequalities. Next, basing on a family of nonempty closed convex subsets of \(\mathcal R^{n}\) and linesearch techniques, we give inner approximation projection algorithms for solving multivalued variational inequalities and the convergence of the algorithms is established under few assumptions.