Moreau-Rockafellar type theorem for convex set functions

DOI10.1016/0022-247X(88)90084-4zbMath0656.90097OpenAlexW1979955085MaRDI QIDQ1110462

Lai-Jiu Lin, Hang-Chin Lai

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(88)90084-4

zbMATH Keywords

Moreau-Rockafellar theoremconvex real- valued set functionsfinite atomless measure spaceFritz John type conditionKuhn-Tucker type condition

Mathematics Subject Classification ID

Convex programming (90C25) Set-valued maps in general topology (54C60) Programming in abstract spaces (90C48)

Related Items (17)

New optimality conditions for a nondifferentiable fractional semipreinvex programming problem ⋮ 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 ⋮ A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions] ⋮ Optimality and duality for multiobjective programming involving subdifferentiable 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 ⋮ Duality without a constraint qualification for minimax fractional programming ⋮ Moreau-Rockafellar type theorems for nonconvex and non-locally lipschitz integral functional onL^p(T,X) ⋮ Alternative theorems and saddlepoint results for convex programming problems of set functions with values in ordered vector spaces

Cites Work

• Optimal constrained selection of a measurable subset
• Duality in mathematical programming of set functions: On Fenchel duality theorem
• On multiple objective programming problems with set functions
• Duality theorem of nondifferentiable convex multiobjective programming
• Epigraphs of convex set functions
• Necessary conditions for optimality of nondifferentiable convex multiobjective programming
• The saddle point theorem of Kuhn and Tucker in ordered vector spaces
• A subgradient duality theorem
• Second order optimality conditions for mathematical prograramming with set functions
• Saddle point and duality in the optimization theory of convex set functions
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