scholarly journals Duality of(h,φ)-Multiobjective Programming Involving Generalized Invex Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
GuoLin Yu

In the setting of Ben-Tal's generalized algebraic operations, this paper deals with Mond-Weir type dual theorems of multiobjective programming problems involving generalized invex functions. Two classes of functions, namely,(h,φ)-pseudoinvex and(h,φ)-quasi-invex, are defined for a vector function. By utilizing these two classes of functions, some dual theorems are established for conditionally proper efficient solution in(h,φ)-multiobjective programming problems.

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.


Author(s):  
P. Pandian

A new approach, namely sum of objectives (SO) method is proposed to finding a fair solution to multi-objective programming problems. The proposed method is very simple, easy to use and understand and also, common approaches. It is illustrated with the help of numerical examples. The fair solution serves more better than efficient solution for decision makers when they are handling multiple objective decision making problems.


Author(s):  
Tadeusz Antczak ◽  
Gabriel Ruiz-Garzón

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs.


2014 ◽  
Vol 505-506 ◽  
pp. 524-527
Author(s):  
Ming Fa Zheng ◽  
Qi Hang He ◽  
Zu Tong Wang ◽  
Dong Qing Su

This paper is devoted to the application of stochastic order to the with stochastic multiobjective programming problem. A new method, called stochastic approach, is originally presented based on stochastic order. The partial Pareto efficient solution is defined first, and then several types of stochastic order from the viewpoint of practical problems are proposed. The results obtained can provide theoretical basis for dealing with the stochastic problems in field of civil engineering and transportation.


1998 ◽  
Vol 98 (3) ◽  
pp. 651-661 ◽  
Author(s):  
R. Osuna-Gómez ◽  
A. Rufián-Lizana ◽  
P. Ruíz-Canales

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