On vector variational inequalities

DOI10.1007/BF02275358zbMath0848.49012OpenAlexW2033931648MaRDI QIDQ5917816

Jen-Chih Yao, Su-Jane Yu

Publication date: 3 November 1996

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

Full work available at URL: https://doi.org/10.1007/bf02275358

zbMATH Keywords

monotone operatorsvector variational inequalitiesvector complementarity problemgeneralized \(L\)-conditionweakly \(C\)-pseudomonotone operatorsweakly \(v\)-coercive conditions

Mathematics Subject Classification ID

Variational inequalities (49J40) Monotone operators and generalizations (47H05)

Related Items (63)

Generalized vector variational-like inequalities and nonsmooth vector optimization problems ⋮ On generalized vector variational-like inequalities ⋮ On the generalized vector variational inequality problem ⋮ Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces ⋮ Generalized vector variational inequalities ⋮ Existence of solutions and algorithms for bilevel vector equilibrium problems: an auxiliary principle technique ⋮ Existence results for VVIP ⋮ Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems ⋮ Generalized vector quasi-variational-like inequality problem: a new approach ⋮ A topological approach for vector quasi-variational inequalities with set-valued functions ⋮ Well-posedness of generalized vector quasivariational inequality problems ⋮ On vector variational \(E\)-inequalities and differentiable vector optimization problem ⋮ Strong vector equilibrium problems ⋮ The convergent behavior for parametric generalized vector equilibrium problems ⋮ Generalized vector version of Minty's lemma and applications. ⋮ Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints ⋮ Upper semicontinuity of solution maps for a parametric weak vector variational inequality ⋮ Survey on vector complementarity problems ⋮ The generalized vector quasi-variational-like inequalities ⋮ Existence of solutions for generalized vector variational-like inequalities ⋮ Existence results for proper efficient solutions of vector equilibrium problems and applications ⋮ Gap functions and error bounds for generalized vector variational inequalities ⋮ A Note On Generalized Vector Variational-Like Inequalities ⋮ Existence results for vector variational inequality problems on Hadamard manifolds ⋮ An existence result for the generalized vector equilibrium problem ⋮ Existence of solutions for nonconvex and nonsmooth vector optimization problems ⋮ A generalized vector variational inequality problem with a set-valued semi-monotone mapping ⋮ Generalized Minty's Lemma for generalized vector equilibrium problems ⋮ Connectedness of the solution sets and scalarization for vector equilibrium problems ⋮ Existence results for systems of vector variational-like inequalities ⋮ Applications of generalized variational and quasivariational inequalities with operator solutions in a TVS ⋮ System of generalized implicit vector quasivariational inequalities ⋮ Continuity of the solution set to parametric weak vector equilibrium problems ⋮ Duality and gap function for generalized multivalued ϵ-vector variational inequality ⋮ Generalized vector variational like inequalities in fuzzy environment ⋮ Efficiency and Henig efficiency for vector equilibrium problems. ⋮ An existence result for generalized vector equilibrium problems without pseudomonotonicity ⋮ Vector equilibrium problems on unbounded sets ⋮ Optimality conditions for vector equilibrium problems ⋮ Existence theorems for generalized vector variational inequalities with a variable ordering relation ⋮ A class of operator equilibrium problems ⋮ On the stability of generalized vector quasivariational inequality problems ⋮ A generalization of Minty's lemma and its applications to generalized mixed vector equilibrium problems ⋮ On the existence of solutions to generalized vector variational-like inequalities ⋮ A note on scalar-valued gap functions for generalized vector variational inequalities ⋮ Existence of solutions of generalized vector variational-type inequalities with set-valued mappings ⋮ On vector variational inequalities in reflexive Banach spaces ⋮ Generalized vector variational and quasi-variational inequalities with operator solutions ⋮ Vector variational inequalities with semi-monotone operators ⋮ Strong vector \(F\)-complementary problem and least element problem of feasible set ⋮ Feasibility and solvability of vector variational inequalities with moving cones in Banach spaces ⋮ On the existence and approximation of solutions for bilevel vector variational inequalities in Banach spaces ⋮ Generalized vector \(F\)-variational inequalities and vectorf-complementarity problems for point-to-set mappings ⋮ A vector auxiliary principle technique approach to systems of mixed vector equilibrium problems ⋮ Vector variational inequalities with cone-pseudomonotone bifunctions ⋮ A vector version of Minty's lemma and applications ⋮ Generalized vector variational inequality and its duality for set-valued maps ⋮ Existence of solutions for vector optimization problems ⋮ Generalized vector quasi-variational-like inequalities ⋮ System of generalised set-valued quasi-variational-like inequalities ⋮ On implicit vector variational inequalities ⋮ Vector variational-type inequalities for set-valued mappings ⋮ Topological variants of vector variational inequality problem

Cites Work

• Unnamed Item
• A generalization of Tychonoff's fixed point theorem
• A complementarity problem in mathematical programming in Banach space
• Existence results for the nonlinear complementarity problem and applications to nonlinear analysis
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• Theory of multiobjective optimization
• Nonlinear complementarity problem of mathematical programming in Banach space
• Complementarity problem and the existence of the post-critical equilibrium state of a thin elastic plate
• Multiple-criteria decision making. Concepts, techniques, and extensions. With the assistance of Yoon-Ro Lee and Antonie Stam
• Monotone (nonlinear) operators in Hilbert space
• Complementarity problems over cones with monotone and pseudomonotone maps
• Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem
• Generalized vector variational inequality and fuzzy extension
• Multi-valued variational inequalities with \(K\)-pseudomonotone operators
• On some non-linear elliptic differential functional equations
• The nonlinear complementarity problem, with applications. I
• On \(M\)-functions and their application to nonlinear Gauss-Seidel iterations and to network flows
• Continuousization of the family of point-to-set maps and its applications
• A vector variational inequality and optimization over an efficient set
• Vector variational inequality and its duality
• Variational Inequalities with Generalized Monotone Operators
• Nonlinear monotone operators and convex sets in Banach spaces
• On the regularity of the solution of a variational inequality
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• The complementarity problem

This page was built for publication: On vector variational inequalities