Relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{\mu }$$\end{document}-quasimonotone variational inequalities in Hadamard manifolds

被引：0
作者：
Alireza Amini-Hararandi
Majid Fakhar
Laleh Nasiri
机构：
[1] University of Isfahan,Department of Mathematics
来源：
Journal of Fixed Point Theory and Applications | 2019年 / 21卷 / 3期
关键词：
Hadamard manifold; variational inequality; relaxed ; -quasimonotone; relaxed ; -quasiconvex; Primary 49J40; Secondary 58E35; 47H04;
D O I：
10.1007/s11784-019-0724-9
中图分类号：
学科分类号：
摘要：
In this article, we introduce relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasimonotone set-valued vector field on Hadamard manifolds and prove the existence of solutions of the Stampacchia variational inequality for such mappings. We also present the notion of relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvexity and show that the Upper Dini and Clarke–Rockafellar subdifferentials of a relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvex function is relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasimonotone. Under relaxed μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mu $$\end{document}-quasiconvexity in the nondifferentiable sense, we establish the connection between the Stampacchia variational inequality problem and a nonsmooth constrained optimization problem.
引用
收藏
相关论文
共 75 条
  • [21] Colao V(2009)Monotone vector fields and the proximal point algorithm on Hadamard manifolds J. Lond. Math. Soc. 79 663-683
  • [22] López G(2011)Weak sharp minima on Riemannian manifolds SIAM J. Optim. 21 1523-1560
  • [23] Marino G(2012)Variational inequalities for set-valued vector fields on Riemannian manifolds: convexity of the solution set and the proximal point algorithm SIAM J. Control Optim. 50 2486-2514
  • [24] Martńn-Márquez V(2016)Gap functions and global error bounds for generalized mixed variational inequalities on Hadamard manifolds J. Optim. Theory Appl. 168 830-849
  • [25] Crouzeix JP(1967)Variational inequalities Commun. Pure Appl. Math. 20 493-519
  • [26] Danildis A(2001)Existence results for densely psudomonotone variational inequalities J. Math. Anal. Appl. 254 291-308
  • [27] Hadjisavvas N(2003)Variational inequalities on Hadamard manifolds Nonlinear Anal. 52 1491-1498
  • [28] Debrunner H(2009)Proximal point methods for quasiconvex and convex functions with bregman distances on Hadamard manifolds J. Convex Anal. 16 49-69
  • [29] Flor P(2012)Full convergence of the proximal point methods for quasiconvex functions on Hadamard manifolds ESAIM Control Optim. Calc. Var. 18 483-500
  • [30] Ferreira OP(2012)Proximal point methods for minimizing quasiconvex locally lipschitz functions on Hadamard manifolds Nonlinear Anal. 75 5924-5932
12345678