On quasimonotone Stampacchia variational inequalities on Hadamard manifolds. (2nd December 2022)

• Record Type: Journal Article
• Authors: Amini-Harandi, A.; Fakhar, M.; Nasiri, L.
• Is Part Of: Optimization. Volume 71:Number 12(2022)
• Page Start: 3695
• Page End: 3708
• Publication Date: 2022-12-02
• Subjects: Hadamard manifold -- Stampacchia variational inequality -- quasimonotone map; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1915311
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, which is deeply inspired from Aussel and Hadjisavvas [On quasimonotone variational inequalities. J Optim Theory Appl. 2004;121:445–450] and Daniilidis and Hadjisavvas [Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions. J Optim Theory Appl. 1999;102(3):525–536], we study the existence of solutions of the Stampacchia variational inequality for a quasimonotone set-valued vector field on a Hadamard manifold. Moreover, the existence results are obtained under weak assumptions like quasimonotonicity and upper-sign continuity. An application of our results is also given.