A preconditioned descent algorithm for variational inequalities of the second kind involving the p-Laplacian operator

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• 作者：Sergio González-Andrade
• 关键词：Variational inequalities ; p ; Laplacian ; Optimization and variational techniques ; Herschel–Bulkley model
• 刊名：Computational Optimization and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：66
• 期：1
• 页码：123-162
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Optimization; Operations Research, Management Science; Operation Research/Decision Theory; Statistics, general; Convex and Discrete Geometry;
• 出版者：Springer US
• ISSN：1573-2894
• 卷排序：66

文摘

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the p-Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian fluids. We study these problems by using a regularization approach, based on a Huber smoothing process. Well posedness of the regularized problems is proved, and convergence of the regularized solutions to the solution of the original problem is verified. We propose a preconditioned descent method for the numerical solution of these problems and analyze the convergence of this method in function spaces. The existence of admissible descent directions is established by variational methods and admissible steps are obtained by a backtracking algorithm which approximates the objective functional by polynomial models. Finally, several numerical experiments are carried out to show the efficiency of the methodology here introduced.