Generalized nonlinear variational-like inequalities

DOI10.1007/s10957-005-2666-1zbMath1080.49010OpenAlexW2066379249MaRDI QIDQ813385

Kang, Shin Min, Liu, Zeqing, Ume, Jeong Sheok

Publication date: 8 February 2006

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-005-2666-1

zbMATH Keywords

algorithmsconvergencefixed pointsexistenceminimax inequalitiesauxiliary principle techniquegeneralized nonlinear variational-like inequalitiesreflexive Banach spaces.

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Programming in abstract spaces (90C48)

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Generalized Eckstein-Bertsekas proximal point algorithm involving \((H,\eta )\)-monotonicity framework ⋮ Auxiliary principle for generalized nonlinear variational-like inequalities ⋮ Topological Approaches for Vector Variational Inequality Problems ⋮ General projection systems and relaxed cocoercive nonlinear variational inequalities ⋮ Generalized nonlinear vector mixed quasi-variational-like inequality governed by a multi-valued map ⋮ Sensitivity analysis for cocoercively monotone variational inclusions and \(( A , \eta)\)-maximal monotonicity ⋮ Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces ⋮ On solvability of a generalized nonlinear variational-like inequality ⋮ Generalized Eckstein-Bertsekas proximal point algorithm based ona-maximal monotonicity design ⋮ On Rockafellar's theorem using proximal point algorithm involving \(H\)-maximal monotonicity framework ⋮ Solvability and algorithms of generalized nonlinear variational-like inequalities in reflexive Banach spaces ⋮ Auxiliary principle for generalized strongly nonlinear mixed variational-like inequalities ⋮ Existence results for generalized nonlinear vector variational-like inequalities with set-valued mapping ⋮ A note on the generalized nonlinear vector variational-like inequality problem

Cites Work

• Nested monotony for variational inequalities over product of spaces and convergence of iterative algorithms
• General variational inequalities in Banach spaces
• Existence and uniqueness of solutions for a general nonlinear variational inequality
• General strongly nonlinear quasivariational inequalities with relaxed Lipschitz and relaxed monotone mappings
• Nonconvex functions and variational inequalities
• On a general nonlinear variational inequality
• A variational-like inequality problem
• Some remarks on variational-like and quasivariational-like inequalities

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