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

被引：14

作者：

Gasinski, Leszek ^{[1
]}

Liu, Zhenhai ^{[2
]}

Migorski, Stanislaw ^{[1
]}

Ochal, Anna ^{[1
]}

Peng, Zijia ^{[2
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[2] Guangxi Univ Nationalities, Coll Sci, Nanning 530006, Guangxi, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 164卷 / 02期

关键词：

Variational inequality; Evolutionary inclusion; Star-shaped set; L-pseudomonotone operator; Clarke subgradient; Distance function; Surjectivity result; EQUATIONS;

D O I：

10.1007/s10957-014-0587-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：514 / 533

页数：20

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