[PDF] Top 20 Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V Type I Invex Functions

... by nonsmooth functions, consequently, the theory of nonsmooth optimization using locally Lipschitz functions was put forward by Clarke in 1980’s see ...convex functions to the ... See full document

... various optimality and duality results have been obtained for multiobjective fractional programming ...[], multiobjective fractional problem and its duality theorems have been ... See full document

... Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational prob- lem are ...Karush-Kuhn-Tucker type optimality conditions, Mond-weir type ... See full document

... sufficient optimality theorems for the multiobjective E-convex programming are established under the weakened assumption of the theorems in Megahed et ...mixed duality for the primal problem is ... See full document

... to nonsmooth multiobjective programming problem involving support ...introduce nonsmooth multiobjective programming problems involving locally Lipschitz functions and ... See full document

... of multiobjective programming, has grown remarkably in different direc- tional in the setting of optimality conditions and duality theory since ...of functions depending on the sign of the ... See full document

... a nonsmooth multiobjective programming problems including support functions with inequality and equality ...sufficient optimality conditions are obtained by using higher-order strong convexity ... See full document

... Univex functions by utilizing a tem- pered fractional difference-differential operator type ...these functions in some optimal problems by exemplifying the settings on the modified ... See full document

... generalized functions. By using the new functions, we have presented a sufficient optimality condition and Wolfe type duality results for a nondifferentiable multiobjective ... See full document

... d-type I func- tions in terms of directional derivative for a multiobjec- tive programming problem and discussed Wolfe type and Mond-Weir type duality ...derived optimality ... 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

... valued functions are not comparable, the concepts of efficiency and proper efficiency are very important in fractional vector optimization ...vector optimization problems ...efficient optimality of ... See full document

... these optimality conditions to define a dual problem and derived duality ...sufficient optimality condition in [5] and also employed the optimality conditions to construct several dual models ... See full document

... a nonsmooth vector optimization problem over ...a nonsmooth vector optimization problem over ...cone- nonsmooth ( F , ρ ) -convex functions of ...several optimality ... See full document

... the optimality conditions and dual theory of multi-objective programming problems involving generalized ...generalized type-I functions are introduced for arcwise connected ... See full document

... various optimality and duality results have been obtained for multiobjective fractional programming ...[4], multiobjective fractional problem and its duality theorems have been ... 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

... convex functions and then neces- sary and sufficient optimality conditions are obtained for nondifferentiable multiobjec- tive problems without the need of a constraint ...some duality results without ... See full document

... constrained optimization problem are all invex for the same η, then both the sufficiency of Kuhn-Tucker conditions and weak and strong Wolfe duality still ...named functions satisfying () ... See full document

... sufficient optimality conditions and ...convex functions have been introduced and applied to mathematical programming problems in the literature ...global optimality of nonlinear programming under the ... See full document