A Class Of Bilevel Multi-follower Programming Problems

The thesis deals with the problem called bilevel multi-follower programming (BMFP).It concerns several particular different bilevel multi-follower programming problems.The duality theory of the problems and necessary and sufficient conditions for them to admit an exact penalty function formulation are presented together with their properties.The organization of this thesis is as follows.In chapter 1,we state plainly the bilevel programming problem and it's research background as an introduction,including the extensive applied fields and bright prospects of the bilevel programming problem and the main research results related to bilevel programming to date.We introduce the problem which we arc going to deal with and some work we do on it.In chapter 2,we investigate the bilevel linear multi-follower programming problem (BLMFP).First,we change the bilevel program BLMFP into an equivalent single level programming problem by using the Karush-Kuhn-Tucker theory and the structure and properties of BLMFP arc prcscntcd.Then,we study the existence of the exact penalty function formulation to BLMFP through discussing the equivalent single level programming. Finally,we address the Lagrangian duality of BLMFP and related duality theorems.In the first section of chapter 3,for the bilevel fractional multi-follower programming problem(BFMFP),wc propose a necessary and sufficient conditions of the existence of optimal solution and a property that an optimal solution of the problem can be attained at a vertex of the polyhedral convex set P under certain condition along the way used in chapter 2.Futhermore,we discuss a necessary and sufficient condition for the problem to admit an exact penalty function approach.In the second section of this chapter,we investigate the bilevel generalized fractional multi-follower programming problem(BGFMFP).Although it can be seen as a extension of problem BFMFP,we use a different approach from the previous one to discuss some equivalent forms of BGFMFP together with the properties of the problem considered.At the same time,by an equivalent d.c. programming problem whose object function is the difference of two convex functions and using the theory of the surrogate dual of d.c. programming,the duality of...