[PDF] Top 20 Sufficiency and duality in multiobjective fractional programming problems involving generalized type I functions

... Fractional programming problems have been studied with different characteristics of functions or diverse ...studied fractional programming problems since ...Kuhn-Tucker ... See full document

... (2015) Sufficiency and Duality for Nonsmooth Multiob- jective Programming Problems Involving Generalized ( , ) ϕ ρ -V-Type I ... See full document

... Bhatia and Sahay [] introduced the following notion of a strict minimizer of order σ with respect to a nonlinear function for the multiobjective programming problem. Definition . A point x ¯ ∈ X is a ... See full document

... introduced generalized d-type I func- tions in terms of directional derivative for a multiobjec- tive programming problem and discussed Wolfe type and Mond-Weir type ... See full document

... A fractional programming problem arises in many types of optimization problem such as portfolio selection, production, information theory and numerous decision making problems in management ...in ... See full document

... the duality theorems for convex minimax pro- gramming problems considered by Weir [3] and relaxed the convexity assumptions in the sufficient optimality of ...introduced generalized second-order ... See full document

... second-order duality for nonlinear programs and obtained second-order duality results under certain ...second-order duality results assuming rather simple ...a fractional programming ... See full document

... of generalized (F, ρ)-convexity, an extension of F- convexity defined by Hanson and Mond [5], and generalized ρ-convexity defined by Vial [14], and he used the concept to obtain some duality ... See full document

... Wolf type non-differentiable second order symmetric primal and dual problems in mathemati- cal ...strong duality theorems were established under second order F-convexity assump- ...dual ... See full document

... minimax fractional programming problem is ...the generalized higher-order η -convexity assumptions on the functions involved, weak, strong and strict converse duality theorems are ... See full document

... ∗ i and λ ∗ i ,i ∈ p, which were in- troduced as a consequence of our indirect approach in [5] requiring two intermediate auxiliary ...∗ i by F i (S ∗ )/G i (S ∗ ), i ∈ p, ... See full document

... nondifferentiable multiobjective fractional programming problems in which every component of objective functions contains a term involving the support function of a compact convex ... See full document

... the multiobjective fractional programming problem (MFP1) considered in Ex- ample ...smooth multiobjective fractional program- ming problems (see, for example, [15, 21–23, 31, 33, ... See full document

... convex functions, Avriel [] first introduced the defi- nition of r-convex functions and established some characterizations and the relations be- tween r-convexity and other generalization of ...r-preinvex ... See full document

... nonsmooth multiobjective programming problems involving locally Lipschitz functions and support ...support functions are ...using generalized convexity and certain ... See full document

... [] generalized these results to static and continuous nonlinear fractional ...the multiobjective case of static nonlinear fractional program, symmetric duality was established under ... See full document

... convex functions, namely B- vex functions which satisfy many of basic properties of convex functions, was introduced by Bector and Singh ...on multiobjective pro- gramming problems and ... See full document

... Symmetric duality in nonlinear programming in which the dual of the dual is the pri- mal was introduced by Dorn ...symmetric duality was developed sig- nificantly by Dantzig et ...more ... See full document

... mathematical programming problem in which the objective function is a ratio of two numerical functions is called a fractional programming ...problem. Fractional pro- gramming is used in ... See full document

... C i = k and S x E ( | j ) 1,2, , ( j = m ) denote the support func- tions of compact convex sets, various researchers have ...proved duality theorems under higher-order ( F , , , ρ ρ d ) -type ... See full document