Two types of minimax theorems for vector-valued functions

DOI10.1007/BF00941571zbMath0696.90060OpenAlexW2068872980MaRDI QIDQ911473

Tamaki Tanaka

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1007/bf00941571

zbMATH Keywords

minimax theoremsvector-valued functionsHausdorff topological vector spaceC-convex functionspointed convex coneSterna-Karwat conditionweak cone saddle points

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Set-valued maps in general topology (54C60) Programming in abstract spaces (90C48) Optimality conditions for minimax problems (49K35) Topological linear spaces and related structures (46A99)

Related Items (11)

Minimax Problems for Set-Valued Mappings ⋮ Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions ⋮ Existence theorems for saddle points of vector-valued maps ⋮ Ky Fan minimax inequalities for set-valued mappings ⋮ Saddle points and minimax theorems for vector-valued multifunctions on \(H\)-spaces ⋮ Minimax inequalities for set-valued mappings ⋮ Some saddle-point theorems for vector-valued functions ⋮ A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions] ⋮ Nash equilibrium and saddle points for multifunctions ⋮ A minimax theorem for vector-valued functions in lexicographic order ⋮ Sufficient conditions in vector-valued maximin problems

Cites Work

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• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Scalarization in vector optimization
• Coincidence theorems, minimax theorems, and variational inequalities
• A note on convex cones in topological vector spaces
• Approaches to the Theory of Optimization

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