On the optimality conditions of vector-valued \(n\)-set functions

DOI10.1016/0022-247X(91)90337-YzbMath0762.90066MaRDI QIDQ1189678

Lai-Jiu Lin

Publication date: 27 September 1992

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

zbMATH Keywords

quasiconvexitypseudoconvexityconvex set functionfinite atomless measure spacevector- valued \(n\)-set functions

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Duality theory (optimization) (49N15)

Related Items (22)

Saddle points and Lagrangian-type duality for discrete minmax fractional subset programming problems with generalized convex functions ⋮ The saddle theorem for multiobjective generalized fractional programming problems with set functions ⋮ Optimality conditions for multiple objective fractional subset programming with \(({\mathcal F},\alpha,\rho,\theta)\)-V-type-I and related non-convex functions ⋮ Duality for multiple objective fractional subset programming with generalized \((\Gamma\mkern-15mu-,\rho,\sigma,\theta)\)-V-Type-I functions ⋮ APPROXIMATE EFFICIENCY FOR n-SET MULTIOBJECTIVE FRACTIONAL PROGRAMMING ⋮ Optimality conditions for multiobjective programming with generalized \(({\mathfrak J},\rho,\theta)\)-convex set functions ⋮ Role of \((\rho , \eta , A)\)-invexity to \(\varepsilon \)-optimality conditions for multiple objective fractional programming ⋮ 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 of vector-valued \(n\)-set functions ⋮ On minimax fractional programming of generalized convex set functions ⋮ On the optimality of differentiable nonconvex \(n\)-set functions ⋮ Optimality conditions for multiple objective fractional subset programming with \((\rho,\sigma,\theta )\)-type-I and related non-convex functions ⋮ Optimality and duality for a multi-objective programming problem involving generalized \(d\)-type-I and related \(n\)-set functions ⋮ Optimality and duality for multiobjective fractional programming involving \(n\)-set functions ⋮ Optimality for nonlinear programs containingn-set functions ⋮ Duality for a minimax programming problem containing \(n\)-set functions ⋮ Unnamed Item ⋮ Lagrange duality in multiobjective fractional programming problems with \(n\)-set functions ⋮ Duality for multiobjective programming involving n-set functions ⋮ Duality for multiobjective fractional programming involvingn-set functions sup^* ⋮ Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized \(({\mathcal F},\alpha,\rho,\theta)\)-\(V\)-convex functions

Cites Work

• Unnamed Item
• Optimality of differentiable, vector-valued n-set functions
• Optimization theory for n-set functions
• Optimal constrained selection of a measurable subset
• Duality in mathematical programming of set functions: On Fenchel duality theorem
• Proper D-solutions of multiobjective programming problems with set functions
• Epigraphs of convex set functions
• Moreau-Rockafellar type theorem for convex set functions
• Optimality for set functions with values in ordered vector spaces
• On the optimality of differentiable nonconvex \(n\)-set functions
• Duality theory in multiobjective programming
• The Multiobjective Optimization Problem of Set Function
• The Fenchel-Moreau Theorem for Set Functions
• Saddle point and duality in the optimization theory of convex set functions

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