The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary

The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name.

 
       
         
    STUDIA MATHEMATICA - Issue no. 3 / 2009  
         
  Article:   STRONG AND CONVERSE FENCHEL DUALITY FOR VECTOR OPTIMIZATION PROBLEMS IN LOCALLY CONVEX SPACES.

Authors:  ANCA GRAD.
 
       
         
  Abstract:  In relation to the vector optimization problem

with f, g proper and cone-convex functions and A : X →Y a linear continuous operator between separated locally convex spaces, we define a general vector Fenchel-type dual problem. For the primal-dual pair we prove weak, and under appropriate regularity conditions, strong and converse duality. In the particular case when the image space is Rm we compare the new dual with two other duals, whose definitions were inspired from [9] and [10], respectively. The sets of Pareto efficient elements of the image sets of their feasible sets through the corresponding objective functions prove to be equal, despite the fact that among the image sets of the problems, strict inclusion usually holds. This equality allows us to derive weak, strong and converse duality results for the later two dual problems, from the corresponding results of the first mentioned one. Our results could be implemented in various practical areas, since they provide sufficient conditions for the existence of optimal solutions for vector optimization problems defined on very general spaces. They can be used in medical areas, for example in the study of chronical diseases and in oncology.

Key words and phrases. conjugate functions, Fenchel duality, vector optimization, weak, strong and converse duality.
 
         
     
         
         
      Back to previous page