Some relations between minty variational-like inequality problems and vectorial optimization problems in Banach spaces

DOI10.1016/j.camwa.2010.09.012zbMath1205.90282OpenAlexW4210713214MaRDI QIDQ623227

Manuel Arana-Jiménez, Antonio Rufián-Lizana, Gabriel Ruiz-Garzón, Lucelina Batista Dos Santos

Publication date: 13 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.09.012

zbMATH Keywords

Banach spacesefficiencyminty variational-like inequality problempseudo-invex functionsvectorial optimization problem

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Programming in abstract spaces (90C48) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items

New optimality conditions for nonsmooth control problems ⋮ Optimality in continuous-time multiobjective optimization and vector variational-like inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some remarks on the Minty vector variational inequality
• The vector complementary problem and its equivalences with the weak minimal element in ordered spaces
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• Exchange price equilibria and variational inequalities
• On Minty vector variational-like inequality
• Pre-invex functions in multiple objective optimization
• Necessary conditions for optimality of nondifferentiable convex multiobjective programming
• Invex functions and generalized convexity in multiobjective programming
• Vector complementarity and minimal element problems
• Minty vector variational inequality, efficiency and proper efficiency
• Generalized invex monotonicity
• Relationships between vector variational-like inequality and optimization problems
• On invex sets and preinvex functions
• A characterization of pseudoinvexity in multiobjective programming
• Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces
• Infine functions and nonsmooth multiobjective optimization problems
• Vector variational-like inequalities and non-smooth vector optimization problems
• Existence of solutions and star-shapedness in Minty variational inequalities
• On some non-linear elliptic differential functional equations
• On vector variational-like inequality problems
• Pre-vector variational inequalities
• On the generalization of a direct method of the calculus of variations
• Convex programming and variational inequalities