IMPROVED DEFINITION OF PROPER EFFICIENCY FOR VECTOR MAXIMIZATION WITH RESPECT TO CONES

被引：200
作者：
BENSON, HP
机构：
[1] University of Florida, Gainesville
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1979年 / 71卷 / 01期
关键词：
D O I：
10.1016/0022-247X(79)90226-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently Borwein has proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone S is any nontrivial, closed convex cone. However, when S is the non-negative orthant, solutions may exist which are proper according to Borwein's definition but improper by Geoffrion's definition. As a result, when S is the non-negative orthant, certain properties of proper efficiency as defined by Geoffrion do not hold under Borwein's definition. To rectify this situation, we propose a definition of proper efficiency for the case when S is a nontrivial, closed convex cone which coincides with Geoffrion's definition when S is the non-negative orthant. The proposed definition seems preferable to Borwein's for developing a theory of proper efficiency for the case when S is a nontrivial, closed convex cone. © 1979.
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页码：232 / 241
页数：10
相关论文
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