Equilibrium problems in Hadamard manifolds

DOI10.1016/j.jmaa.2011.11.001zbMath1273.49015OpenAlexW2058655938MaRDI QIDQ662049

Victoria Martín-Márquez, Genaro López-Acedo, Vittorio Colao, Giuseppe Marino

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.11.001

zbMATH Keywords

resolventfixed pointvariational inequalityNash equilibriumequilibrium problemHadamard manifoldfirmly nonexpansive mapping

Mathematics Subject Classification ID

Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Global Riemannian geometry, including pinching (53C20) Existence theories in calculus of variations and optimal control (49J99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singularities of monotone vector fields and an extragradient-type algorithm
• Monotone and accretive vector fields on Riemannian manifolds
• Resolvents of set-valued monotone vector fields in Hadamard manifolds
• Existence of solutions for variational inequalities on Riemannian manifolds
• A generalization of Tychonoff's fixed point theorem
• Iterative algorithms for nonexpansive mappings on Hadamard manifolds
• Equilibrium programming using proximal-like algorithms
• Smooth nonlinear optimization of \(\mathbb R^n\)
• A remark on vector-valued equilibria and generalized monotonicity
• Nonsmooth analysis and Hamilton--Jacobi equations on Riemannian manifolds
• Monotonicity, resolvents and Yosida approximations of operators on Hilbert manifolds.
• New existence results for equilibrium problems
• Variational inequalities on Hadamard manifolds
• An iterative method for finding common solutions of equilibrium and fixed point problems
• Sectional curvatures in nonlinear optimization
• Convex- and monotone-transformable mathematical programming problems and a proximal-like point method
• Convergence theorems for sequences of nonlinear operators in Banach spaces
• Generalized monotone bifunctions and equilibrium problems
• An fixed point theorem
• Non-cooperative games
• Minimax and Variational Inequalities for Compact Spaces
• Location of Nash equilibria: A Riemannian geometrical approach
• Monotone vector fields and the proximal point algorithm on Hadamard manifolds
• The Asymptotic Behavior of Firmly Nonexpansive Mappings
• Proximal Point Algorithm On Riemannian Manifolds
• Iterative Algorithms for Equilibrium Problems
• Games with non-convex strategy sets
• Fixed Point Theorems for Multi-Valued Transformations
• Inexact implicit method with variable parameter for mixed monotone variational inequalities

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