On the projection of the efficient set and potential applications

作     者：Kim, NTB Muu, L 

作者机构：Hanoi Inst Math Hanoi 10000 Vietnam 

出 版 物：《OPTIMIZATION》 (最优化)

年 卷 期：2002年第51卷第2期

页      面：401-421页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：National Basic Program in Natural Science 

主　　题：multiple objective linear programming efficient set dimension reduction projection outer and inner approximation optimization over the efficient set 

摘      要：We study the efficient set X-E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X-E) of X-E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X-E). Application to optimization over the efficient set for a multiple objective linear program is considered.