Research On Several Types Of Optimal Solutions To Interval Linear Programming

High-profile optimization problems have already been permeated into production, management,decision-making, business and so on. According to the deterministic of cer-tainty, optimization problems can be divided into deterministic optimization problems and uncertain optimization problems. According to the different forms of the parameters expressions, uncertain optimization problems can be divided into Stochastic Program-ming, Fuzzy Programming and Interval Programming. Stochastic programming need to get precise probability distribution of random parameter, and fuzzy programming need to get the membership functions of fuzzy parameters, which are usually unknown. However interval programming only need to obtain the change bounds of the uncertain parameters which are easy to obtain in actual application. Therefore in recent years, the program-ming with interval coefficients has been attracting more and more attentions at home and abroad. Based on the existing theory of interval linear programming, this paper makes the following work:Chapter1, the introduction introduces the basic definition of the interval quantity and related symbol representation. The practical significance and research status of some related issues of interval linear programming at home and abroad have been described in this section;Chapter2proposes the construction problem of constraint matrices corresponded by an optimal solution. And the construction method of constraint matrices corresponded by the optimal solution to various types of interval linear programming are developed;Chapter3introduces the new concepts of optimal solution in a more general and unified framework. And the necessary and sufficient conditions for checking that a vector is a (b(?), A(?), c(?)-optimal solution, an (A(?), b(?), c(?))-optimal solution or a (b(?), A(?), c(?))-optimal solution are developed by tangent cone in type A interval linear programming;Chapter4discusses the robust optimization of a solution to interval linear program-ming. And the necessary and sufficient conditions for checking a solution with robust optimization are developed based on the K-T conditions;Chapter5proposes the weak optimal inverse problem of interval linear program-ming. And a method for solving it is developed; Chapter6summarizes the main contents of this paper and prospects the future workon the basis of existing research.