POSITIVE PROPER EFFICIENT POINTS AND RELATED CONE RESULTS IN VECTOR OPTIMIZATION THEORY

被引：48

作者：

DAUER, JP ^{[1
]}

GALLAGHER, RJ ^{[1
]}

机构：

[1] UNIV MONTANA,DEPT MATH SCI,MISSOULA,MT 59812

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1990年 / 28卷 / 01期

关键词：

D O I：

10.1137/0328008

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Positive proper efficient points are defined as solutions of appropriate linear scalar optimization problems. A geometric characterization of positive proper efficient points is given as well as conditions under which the set of positive proper efficient points is dense in the set of all efficient points. It is shown that these results are applicable in the normed vector lattices C[a, b], lp, and Lp for 1 ≤ p ≤ ∞, and that previous related results, which required the ordering cone to have a compact or weak-compact base, and not applicable in many normed vector lattices, including C[a, b], lp, and Lp for 1 ≤ p ≤ ∞.

引用

页码：158 / 172

页数：15

共 27 条

[1]

Arrow K.J., 1953, CONTRIB THEORY GAMES, V2, P87

[2] IMPROVED DEFINITION OF PROPER EFFICIENCY FOR VECTOR MAXIMIZATION WITH RESPECT TO CONES [J].