Journal Article10.1007/BF00939217
Proper D-solutions of multiobjective programming problems with set functions
Wei-Shen Hsia,T. Y. Lee +1 more
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TL;DR: A special class of solutions for multiobjective programming problems with set functions is considered in this article, where a subset of nondominated solutions, called properD-solution set, with respect to a given domination structure is characterized under two situations, with and without inequality constraints.
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Abstract: A special class of solutions for multiobjective programming problems with set functions is considered. A subset of nondominated solutions, called properD-solution set, with respect to a given domination structure is characterized under two situations, with and without inequality constraints.
read more
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A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions
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Optimality conditions and duality for multiobjective measurable subset selection problems
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Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (ϝ, α, ϱ, θ)-V-convex functions
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References
Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
TL;DR: In this article, a structure of domination over the objective space and the geometry of the set of all non-convex solutions for decision problems with multiple non-commensurable objectives is proposed.
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On multiple objective programming problems with set functions
TL;DR: In this article, the convexity of a subset of a σ-algebra is defined and a Farkas-Minkowski theorem for set functions is proved.
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Saddle point and duality in the optimization theory of convex set functions
Hang-Chin Lai,Shu-Shih Yang +1 more
TL;DR: In this article, it is proved that a minimization problem of a set function G has an optimal solution if and only if the Lagrangian on X L,(X, ©, m) has a saddle point (Qo, f0) such that G(Q0) = inf GQ(Q), = inf L(Q;f0) where /0 is an element of the conjugate set ©* (for the definition, see the later context).
37
Epigraphs of convex set functions
TL;DR: In this paper, the authors characterized a convex set function by its epigraph and derived a Fenchel duality theorem for set functions with a functional in L∞ and showed that the w∗-closure of such a functional is convex functional.
33
Second order optimality conditions for mathematical prograramming with set functions
TL;DR: In this paper, the second order necessary and sufficient conditions are given for a class of optimization problems involving optimal selection of a measurable subset from a given measure subspace subject to set function inequalities.
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