《最优值意义下半定规划反问题的结构与求解》由会员分享，可在线阅读，更多相关《最优值意义下半定规划反问题的结构与求解（39页珍藏版）》请在金锄头文库上搜索。
1、河北工业大学 硕士学位论文 最优值意义下半定规划反问题的结构与求解 姓名：褚洪生 申请学位级别：硕士 专业：计算数学 指导教师：刘新为 20070601 ? ? ? ? ? ? ? ? ? ? ?Iyengar?Kang13? Guan?Diao14?Zhang?Liu5? ?Ahmed?Guan6? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? i ? ? THE STRUCTURE AND SOLUTION OF THE INVERSE OPTIMAL VALUE SEMIDEFINITE PROGRAMMING PROBLEM ABSTRACT ii ? The inver
2、se optimal value semidefi nite programming problems are pro- posed in this paper. Semidefi nite 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 i
3、n our ability to solve such problems effi ciently in theory and in practice. Inverse optimization problems are widely used in the ap- plication areas. Unfortunately, recent research interests are mostly confi ned in a limited area. Most of the researchers just work with the inverse lin- ear programm
4、ing problems. Iyengar and Kang 13 pointed out that the inverse semidefi nite programming problems can be applied to many areas. Guan and Diao14 considered about the inverse semidefi nite programming problems, which is based on the discussion of Zhang and Liu5about the inverse linear programming prob
5、lems. This paper is inspired by the work of Ahmed and Guan6, in which they proposed a new kind of inverse op- timization problemsinverse optimal value linear programming problem. We consider the inverse optimal value problem based on semidefi nite pro- gramming problems, and prove that this kind of
6、problem can be solved by calculating some linear or nonlinear semidefi nite programming problems. This dissertation is arranged as follows, the fi rst chapter of the disser- tation introduces the background of the inverse semidefi nite programming problems, then some basic knowledge of semidefi nite
7、 programming prob- lems 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 semidefi nite pro- gramming problems in chapter 4. We describe an algorit
8、hm for the inverse optimal value semidefi nite programming problems. Some preliminary nu- merical results are reported. KEY WORDS: Semidefi nite programming, inverse problem, inverse op- timization, linear programming, inverse optimal value problem iii ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1992?Burton?Toint2? ? ? ? ? ? P :min x cTx|x X, ?x X?c?x?P? ?c? c? kc ckp? ?Burton?Toint23?l2? 1 ? ? ? ?Zhang?Liu45?l1?l?Yang? Zhang15?2001?Ahuja?Orlin1? ? ?P?l1?l? ?2005?Ahmed?Guan6? ?P?z? ?C?c C?P?z? ?Ahmed?Guan?6? ?Ahmed?Guan? ? ? ?z i ? z i ? ? ?Paleologo?Takriti7?Ahmed ?Guan? ? ? ? ?
