The Fenchel-Moreau Theorem for Set Functions

DOI10.2307/2047532zbMath0645.49009OpenAlexW4255454061MaRDI QIDQ3788604

Hang-Chin Lai, Lai-Jui Lin

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047532

zbMATH Keywords

subdifferentialconjugate functionalFenchel-Moreau theorem for set functions

Mathematics Subject Classification ID

Convex programming (90C25) Nonsmooth analysis (49J52) Set-valued functions (26E25) Set-valued maps in general topology (54C60) Methods involving semicontinuity and convergence; relaxation (49J45) Duality theory (optimization) (49N15) Convexity of real functions in one variable, generalizations (26A51)

Related Items (13)

A primal-dual algorithm for nonnegative \(N\)-th order CP tensor decomposition: application to fluorescence spectroscopy data analysis ⋮ On several results about convex set functions ⋮ Optimality for set functions with values in ordered vector spaces ⋮ Optimality conditions for multiobjective programming with generalized \(({\mathfrak J},\rho,\theta)\)-convex set functions ⋮ Duality theorems for convex and quasiconvex set functions ⋮ Duality theorems of vector-valued \(n\)-set functions ⋮ On minimax fractional programming of generalized convex set functions ⋮ On the optimality conditions of vector-valued \(n\)-set functions ⋮ On the optimality of differentiable nonconvex \(n\)-set functions ⋮ Minimax fractional programming for \(n\)-set functions and mixed-type duality under generalized Invexity ⋮ Optimality of differentiable, vector-valued n-set functions ⋮ Duality for a minimax programming problem containing \(n\)-set functions ⋮ Alternative theorems and saddlepoint results for convex programming problems of set functions with values in ordered vector spaces

Cites Work

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• Optimal constrained selection of a measurable subset
• Duality in mathematical programming of set functions: On Fenchel duality theorem
• A generalization of the Fenchel-Moreau theorem
• On multiple objective programming problems with set functions
• Convex programming on spaces of measurable functions
• A duality theorem for a convex programming problem in order complete vector lattices
• Second order optimality conditions for mathematical prograramming with set functions
• Mathematical methods of game and economic theory
• Saddle point and duality in the optimization theory of convex set functions

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