[PDF] Top 20 Optimality Conditions in Nondifferentiable G Invex Multiobjective Programming

... for invex functions. Hanson 3 introduced the concepts of invex functions, and Type I, Type II functions were introduced by Hanson and Mond ...type optimality conditions for cone invex ... See full document

... differentiable multiobjective programming ...established optimality conditions and duality results in nonsmooth scalar programming assuming Clarke’s generalized subgradients under type I ... See full document

... ficient optimality conditions for efficient and properly ef- ficient solutions to the problem are established involving new classes of semidirectionally differentiable generali- zed type I ... See full document

... called invex function, which was firstly introduced by Hanson ...the optimality conditions for nonlinear programming ...second-order invex functions and dealt with the optimal solution ... See full document

... stationary conditions for the MOSIPVC and establish the strong KKT type sufficient optimality conditions for the MOSIPVC under generalized convexity ...KKT optimality conditions for the ... See full document

... Kuhn-Tucker conditions [, ] for an optimization problem with an interval-valued objective function under the assumption of ...Kuhn-Tucker optimality conditions in multiobjective ... See full document

... sufficient conditions are obtained for K -invex functions in ...of G-invex functions is introduced by Antczak [3]. Optimality and duality for differen- tiable ... See full document

... sufficient optimality conditions and duality the- orems for nonlinear mathematical programming problems under the assumptions of introduced ... See full document

... the optimality condi- tions of (FP), we can find a feasible solution of ...reasonable conditions are fulfilled, then (FP) and (D) have the same optimal value, and we have the following strong duality ... See full document

... sufficient conditions for an optimal solution to the minimax fractional prob- lem and then established weak, strong, and strict converse duality theorems for the prob- lem and its dual problem under B-(p, ... See full document

... convexity conditions. Consequently, several classes of (generalized) invex functions have been introduced in the ...Kuhn-Tucker conditions are sufficient for (global) optimality of non-linear ... See full document

... necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower ... See full document

... nonsmooth multiobjective programming problem involving support ...nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions for inequality and ... See full document

... sufficient optimality theorem is given by using this characterization and E- convexity ...for multiobjective E-convex ...the multiobjective case are estab- lished under the weakened assumption of the ... See full document

... mathematical programming problems, various generalized convexity notations have been ...mathematical programming has not only used in many theoretical and computational developments in mathematical ... See full document

... In this paper, we have defined a class of new generalized functions. By using the new functions, we have presented a sufficient optimality condition and Wolfe type duality results for a nondifferentiable ... See full document

... We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of properly efficient solutions are presented. We ... See full document

... The paper is organized as follows. In Section , we recall some known concepts in the lit- erature and then introduce the concept of strong invexity of order σ for a locally Lipschitz function and its generalizations. ... See full document

... dual for a nonlinear optimization problem, { min f (x), subject to g(x) ≤ }. Inspired by this concept, many researchers have worked in this direction. Chen [] has formulated higher- order multiobjective ... See full document

... nonlinear programming more than one ratio of two functions is to be minimized or ...called multiobjective fractional programming ...Fractional programming has an important significance in ... See full document