On quasimonotone Stampacchia variational inequalities on Hadamard manifolds

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;...

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Bibliographic Details
Published inOptimization Vol. 71; no. 12; pp. 3695 - 3708
Main Authors Amini-Harandi, A., Fakhar, M., Nasiri, L.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.12.2022
Taylor & Francis LLC
Subjects
Fields (mathematics)
Hadamard manifold
Inequalities
Manifolds
quasimonotone map
Stampacchia variational inequality
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Summary: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2021.1915311