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

Leszek Gasiński (), Zhenhai Liu (), Stanisław Migórski (), Anna Ochal () and Zijia Peng ()
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Leszek Gasiński: Jagiellonian University
Zhenhai Liu: College of Sciences, Guangxi University for Nationalities
Stanisław Migórski: Jagiellonian University
Anna Ochal: Jagiellonian University
Zijia Peng: College of Sciences, Guangxi University for Nationalities

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 7, 514-533

Abstract: Abstract 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.

Keywords: Variational inequality; Evolutionary inclusion; Star-shaped set; $$L$$ L -pseudomonotone operator; Clarke subgradient; Distance function; Surjectivity result; 47J20; 47J35; 35K86 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-014-0587-6

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