Maximal points with respect to cone dominance in Banach spaces and their existence

DOI10.1007/BF00934893zbMath0529.46023MaRDI QIDQ787438

N. E. Zubov

Publication date: 1984

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

zbMATH Keywords

optimality conditionsconical frontierconical support pointsGeoffrion's characterization of proper efficiencymaximal points with respect to cone dominance in Banach spacesmaximizing points

Mathematics Subject Classification ID

Banach lattices (46B42) Existence theories for problems in abstract spaces (49J27) Ordered topological linear spaces, vector lattices (46A40)

Related Items (11)

Characterizations of some remarkable classes of cones ⋮ Remarks on convex cones ⋮ A minimax theorem for vector-valued functions ⋮ Density of the set of positive proper minimal points in the set of minimal points ⋮ The domination property for efficiency in locally convex spaces ⋮ A minimax theorem for vector-valued functions. II ⋮ A minimax theorem for \(\overline{L}^0\)-valued functions on random normed modules ⋮ Existence of maximal points with respect to ordered bipreference relations ⋮ Pareto optimization in topological vector spaces ⋮ Inclusion theorems for non-explosive and strongly exposed cones in normed spaces ⋮ Comparison of existence results for efficient points

Cites Work

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• Connectedness of the set of nondominated outcomes in multicriteria optimization
• Duality theory in multiobjective programming
• The structure of admissible points with respect to cone dominance
• Proper efficiency and the theory of vector maximization
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Semi-Compactness with Respect to a Euclidean Cone
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• Existence Theorems for Pareto Optimization; Multivalued and Banach Space Valued Functionals

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