On Minty vector variational-like inequality

DOI10.1016/j.camwa.2007.12.011zbMath1155.90458OpenAlexW2062473737MaRDI QIDQ1004671

Xiao Gang, San-Yang Liu

Publication date: 12 March 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2007.12.011

zbMATH Keywords

efficient solutionvector optimization problemvector variational-like inequality\(\eta \)-pseudomonotonepseudoinvex

Mathematics Subject Classification ID

Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (13)

On minty variational principle for quasidifferentiable vector optimization problems ⋮ On Minty variational principle for nonsmooth vector optimization problems with approximate convexity ⋮ On vector variational-like inequalities and vector optimization problems with \(\left ({G,\alpha} \right)\)-invexity ⋮ Differential properties and optimality conditions for generalized weak vector variational inequalities ⋮ Some relations between minty variational-like inequality problems and vectorial optimization problems in Banach spaces ⋮ On approximately star-shaped functions and approximate vector variational inequalities ⋮ Generalized vector variational-like inequalities and vector optimization ⋮ Nonsmooth variational-like inequalities and nonsmooth vector optimization ⋮ On local quasi efficient solutions for nonsmooth vector optimization problems ⋮ A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems ⋮ Nonsmooth quasi-variational-like inequalities with applications to nonsmooth vector quasi-optimization ⋮ Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization ⋮ Optimality in continuous-time multiobjective optimization and vector variational-like inequalities

Cites Work

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• Some remarks on the Minty vector variational inequality
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• On generalized strong vector variational-like inequalities in Banach spaces
• Vector variational-like inequalities and non-smooth vector optimization problems
• Existence of solutions and star-shapedness in Minty variational inequalities
• A class of nonconvex functions and mathematical programming
• On the generalization of a direct method of the calculus of variations
• Characterizations and applications of prequasi-invex functions.

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