Optimality for set functions with values in ordered vector spaces

DOI10.1007/BF00939803zbMath0664.90094OpenAlexW1975298688MaRDI QIDQ1115816

Lai-Jiu Lin, Hang-Chin Lai

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf00939803

zbMATH Keywords

dualitynormal coneslocally convex Hausdorff topological vector spacesweak saddle pointsMoreau-Rockafellar theoremorder-complete vector latticesfinite atomless measure spaceconvex subfamilyFritz John type optimality conditionKuhn-Tucker type optimality conditionstrictly convex set functionsweak subdifferentials

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Duality theory (optimization) (49N15) Duality theory for topological vector spaces (46A20) Ordered topological linear spaces, vector lattices (46A40) Optimality conditions for problems in abstract spaces (49K27)

Related Items (12)

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 ⋮ A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions] ⋮ Duality theorems of vector-valued \(n\)-set functions ⋮ On the optimality conditions of vector-valued \(n\)-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 of differentiable, vector-valued n-set functions ⋮ Duality for a minimax programming problem containing \(n\)-set functions ⋮ Unnamed Item ⋮ Alternative theorems and saddlepoint results for convex programming problems of set functions with values in ordered vector spaces ⋮ 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
• 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
• Moreau-Rockafellar type theorem for convex set functions
• More on subgradient duality
• Duality theory for maximizations with respect to cones
• A duality theorem for a convex programming problem in order complete vector lattices
• The saddle point theorem of Kuhn and Tucker in ordered vector spaces
• Second order optimality conditions for mathematical prograramming with set functions
• The Multiobjective Optimization Problem of Set Function
• The Fenchel-Moreau Theorem for Set Functions
• A duality theorem for non-linear programming
• A duality theorem for nondifferentiable convex programming with operatorial constraints
• Saddle point and duality in the optimization theory of convex set functions

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