Hemivariational Inequality Approach to Evolutionary Constrained Problems on Star-Shaped Sets

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• 作者：Leszek Gasiński ; Zhenhai Liu…
• 关键词：Variational inequality ; Evolutionary inclusion ; Star ; shaped set ; $$L$$ L ; pseudomonotone operator ; Clarke subgradient ; Distance function ; Surjectivity result ; 47J20 ; 47J35 ; 35K86
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：164
• 期：2
• 页码：514-533
• 全文大小：228 KB
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• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, we consider a nonconvex evolutionary constrained problem for a star-shaped set. The problem is a generalization of the classical evolution variational inequality of parabolic type. We provide an existence result; the proof is based on the hemivariational inequality approach, a surjectivity theorem for multivalued pseudomonotone operators in reflexive Banach spaces, and a penalization method. The admissible set of constraints is closed and star-shaped with respect to a certain ball; this allows one to use a discontinuity property of the generalized Clarke subdifferential of the distance function. An application of our results to a heat conduction problem with nonconvex constraints is provided.