The Structure And Solution Of The Inverse Optimal Value Semidefinite Programming Problem

The inverse optimal value semidefinite programming problems are proposed in this paper. Semidefinite programming problems have been studied extensively in the last few years. Part of the reason for the interest stems from the applicability of problems to diverse areas and partly from the great advances in our ability to solve such problems efficiently in theory and in practice. Inverse optimization problems are widely used in the application areas. Unfortunately, recent research interests are mostly confined in a limited area. Most of the researchers just work with the inverse linear programming problems. Iyengar and Kang pointed out that the inverse semidefinite programming problems can be applied to many areas. Guan and Diao considered about the inverse semidefinite programming problems, which is based on the discussion of Zhang and Liu about the inverse linear programming problems. This paper is inspired by the work of Ahmed and Guan, in which they proposed a new kind of inverse optimization problems—inverse optimal value linear programming problem. We consider the inverse optimal value problem based on semidefinite programming problems, and prove that this kind of problem can be solved by calculating some linear or nonlinear semidefinite programming problems.This dissertation is arranged as follows, the first chapter of the dissertation introduces the background of the inverse semidefinite programming problems, then some basic knowledge of semidefinite programming problems is given in the second chapter. In the third part of the dissertation, we discribe the inverse linear programming problems. As the heart of the dissertation, we give a detailed discussion of the inverse semidefinite programming problems in chapter 4. We describe an algorithm for the inverse optimal value semidefinite programming problems. Some preliminary numerical results are reported.