Conjugate duality in vector optimization and some applications to the vector variational inequality

DOI10.1016/j.jmaa.2006.06.093zbMath1154.90613OpenAlexW1999982999MaRDI QIDQ1001257

Radu Ioan Boţ, Lkhamsuren Altangerel, Gert Wanka

Publication date: 17 February 2009

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.2006.06.093

zbMATH Keywords

vector optimizationvector variational inequalityconjugate dualitygap functionperturbation functionconjugate map

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46)

Related Items (13)

Generalized Lagrangian duality in set-valued vector optimization via abstract subdifferential ⋮ Conjugate dual problems in constrained set-valued optimization and applications ⋮ Partial order relations on family of sets and scalarizations for set optimization ⋮ Sensitivity analysis for a Lagrange dual problem to a vector optimization problem ⋮ Optimality conditions in set-valued optimization problem with respect to a partial order relation via directional derivative ⋮ Duality in vector optimization via augmented Lagrangian ⋮ Saddle points and gap functions for vector equilibrium problems via conjugate duality in vector optimization ⋮ The gap function for optimization problems in Banach spaces ⋮ On gap functions for nonsmooth multiobjective optimization problems ⋮ Duality and gap function for generalized multivalued ϵ-vector variational inequality ⋮ A vectorization for nonconvex set-valued optimization ⋮ An Oriented Distance Function Application to Gap Functions for Vector Variational Inequalities ⋮ Gap functions for generalized vector equilibrium problems via conjugate duality and applications

Cites Work

• Merit functions for general variational inequalities
• Theory of multiobjective optimization
• On supremum of a set in a multidimensional space
• General variational inequalities
• Conjugate maps and duality in multiobjective optimization
• Conjugate duality in vector optimization
• A generalization of Fenchel duality in set-valued vector optimization
• On vector variational inequalities: Application to vector equilibria
• Some developments in general variational inequalities
• New constraint qualification and conjugate duality for composed convex optimization problems
• Vector variational inequality as a tool for studying vector optimization problems
• ON THE CONSTRUCTION OF GAP FUNCTIONS FOR VARIATIONAL INEQUALITIES VIA CONJUGATE DUALITY
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