Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods

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• 作者：Javad Balooee
• 关键词：Regularized nonconvex mixed variational inequalities ; Auxiliary principle technique ; Prox ; regularity ; Nonconvex sets ; Predictor–corrector methods ; Convergence analysis
• 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：774-801
• 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

In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new predictor corrector methods for solving such class of regularized nonconvex mixed variational inequalities are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity of the operator involved in regularized nonconvex mixed variational inequalities. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.