On multiple objective programming problems with set functions

TL;DR: In this paper, the concept of quasiconvexity and pseudoconvexness of set functions is introduced and properties and relations between these generalized convex set functions are investigated.

TL;DR: Under different forms of ρ-convexity conditions for n-set functions duality results are established for multiobjective fractional programming problems involving differentiable n-sets functions as discussed by the authors.

TL;DR: The purpose of this paper is to present a survey of optimality conditions and duality for programming problems involving set and n -set functions.

TL;DR: A new class of generalized convex n-set functions, called (,ρ, σ, θ)-V-Type-I and related non-convex functions are used to establish appropriate duality theorems for three parametric and three semi-parametric dual models to the primal problem.

TL;DR: In this paper, the generalized Fenchel theorem was proved for the optimization problem of a set function defined on a family of measurable subsets in an atomless finite measure space (X, a, m).

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).