Existence results for a class of hemivariational inequality problems on Hadamard manifolds. (2nd July 2016)

• Record Type: Journal Article
• Authors: Tang, Guo-ji; Zhou, Li-wen; Huang, Nan-jing
• Is Part Of: Optimization. Volume 65:Number 7(2016)
• Page Start: 1451
• Page End: 1461
• Publication Date: 2016-07-02
• Subjects: Hemivariational inequality -- generalized directional derivative -- locally Lipschitz function -- Fan-KKM lemma -- Hadamard manifold; 49J40 -- 47J20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1147036
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, a class of hemivariational inequality problems are introduced and studied on Hadamard manifolds. Using the properties of Clarke's generalized directional derivative and Fan-KKM lemma, an existence theorem of solution in connection with the hemivariational inequality problem is obtained when the constraint set is bounded. By employing some coercivity conditions and the properties of Clarke's generalized directional derivative, an existence result and the boundedness of the set of solutions for the underlying problem are investigated when the constraint set is unbounded. Moreover, a sufficient and necessary condition for ensuring the nonemptiness of the set of solutions concerned with the hemivariational inequality problem is also given.