Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions

DOI10.1007/BF02191669zbMath0826.90102OpenAlexW2020867778MaRDI QIDQ1331095

Tamaki Tanaka

Publication date: 9 August 1994

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

Full work available at URL: https://doi.org/10.1007/bf02191669

zbMATH Keywords

Browder's coincidence theoremgeneralized minimax theoremTychonoff's fixed-point theoremvector- valued functionweak type generalized saddle points

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Set-valued functions (26E25) Convexity of real functions of several variables, generalizations (26B25)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two types of minimax theorems for vector-valued functions
• A minimax theorem for vector-valued functions. II
• Theory of multiobjective optimization
• On existence of cone-maximal points in real topological linear spaces
• Some minimax problems of vector-valued functions
• On the image of a constrained extremum problem and some applications to the existence of a minimum
• A minimax theorem for vector-valued functions
• Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces
• Some minimax theorems in vector-valued functions
• Duality theory in multiobjective programming
• Connectedness of the efficient point sets in quasiconcave vector maximization
• Cyclical coincidence of multivalued maps
• Minimax type theorems for n-valued functions
• A characterization of generalized saddle points for vector-valued functions via scalarization
• Ordered linear spaces
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Ein Fixpunktsatz
• Non-cooperative games
• Scalarization in vector optimization
• Coincidence theorems, minimax theorems, and variational inequalities
• Existence and characterization of efficient decisions with respect to cones
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• An Existence Theorem in Vector Optimization
• Convex Analysis

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