On sufficiency in multiobjective programming involving generalized (G,C,ρ)-type I functions

Sufficiency in multiobjective subset programming involving generalized type-I functions

In this paper, sufficient optimality conditions for a multiobjective subset programming problem are established under generalized (F ,α, ρ,d)-type-I functions.

Sufficiency and duality in multiobjective fractional programming problems involving generalized type I functions

*Correspondence: [email protected] Chung-Jen Junior College of Nursing, Health Sciences and Management, Dalin, 62241, Taiwan Abstract In this paper, we establish sufficient optimality conditions for the (weak) efficiency to multiobjective fractional programming problems involving generalized (F,α,ρ ,d)-V-type I functions. Using the optimality conditions, we also investigate a parametric-type dua...

Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions

In this paper, new classes of generalized (F,α,ρ, d)-V -type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.

MULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEMS INVOLVING GENERALIZED d - TYPE - I n - SET FUNCTIONS

For 1 1 ( ) ( )∈! m m m x = x ,...,x , y = y ,...,y we put ≤ x y iff i i x y ≤ for each { } 1 2 ∈ i M = , ,...,m ; ≤ x y iff ≤ i i x y for each i M ∈ , with x y; x < y ≠ iff i i x < y for each i M ∈ . We write + ∈! m x iff 0 ≥ x . For an arbitrary vector n x∈! and a subset J of the index set { } 1 2 n , ,..., , we denote by J x the vector with components j x , j J ∈ . Let ( ) μ X , Γ, be a fini...

Generalized -Type I Univex Functions in Multiobjective Optimization