A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case

DOI10.1080/02331934.2015.1132217zbMath1338.90319OpenAlexW2292949499MaRDI QIDQ2810102

Refail Kasimbeyli, Nergiz Kasimbeyli, Musa A. Mammadov

Publication date: 31 May 2016

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102050

zbMATH Keywords

vector optimizationdensity theoremproper efficiencynonlinear separation theoremaugmented dual cone

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items (4)

Density and connectedness of optimal points with respect to improvement sets ⋮ Weak Henig proper solution sets for set optimization problems ⋮ Duality in nonconvex vector optimization ⋮ Separation theorems for nonconvex sets and application in optimization

Cites Work

• Properly optimal elements in vector optimization with variable ordering structures
• On the density of positive proper efficient points in a normed space
• Optimality conditions in nonconvex optimization via weak subdifferentials
• An improved definition of proper efficiency for vector maximization with respect to cones
• Proper efficiency with respect to cones
• The structure of admissible points with respect to cone dominance
• Some more density results for proper efficiencies
• Density theorems for generalized Henig proper efficiency
• Proper efficiency in locally convex topological vector spaces
• The domination property for efficiency in locally convex spaces
• Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces
• Maximal points of convex sets in locally convex topological vector spaces: generalization of the Arrow-Barankin-Blackwell theorem
• Existence and characterization theorems in nonconvex vector optimization
• A conic scalarization method in multi-objective optimization
• On Weak Subdifferentials, Directional Derivatives, and Radial Epiderivatives for Nonconvex Functions
• A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization
• A Generalization of a Theorem of Arrow, Barankin, and Blackwell
• The geometry of Pareto efficiency over cones
• Proper Efficient Points for Maximizations with Respect to Cones
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• Super Efficiency in Vector Optimization
• Density Results for Proper Efficiencies
• Two Generalizations of a Theorem of Arrow, Barankin, and Blackwell
• On the Existence of Pareto Efficient Points
• A new ABB theorem in normed vector spaces
• On the density of proper efficient points
• A New Abb Theorem In Banach Spaces
• Radial epiderivatives and set-valued optimization

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