Acta mathematica scientia, Series B >
NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS
Received date: 2012-06-14
Revised date: 2014-06-09
Online published: 2014-09-20
Supported by
This research was supported by the National Natural Science Foundation of China (10871141).
Let (E, ξ) = ind(En, ξn) be an inductive limit of a sequence (En, ξn)n∈N of locally convex spaces and let every step (En, ξn) be endowed with a partial order by a pointed convex (solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (Sn)n∈N of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.
QIU Jing-Hui . NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS[J]. Acta mathematica scientia, Series B, 2014 , 34(5) : 1670 -1676 . DOI: 10.1016/S0252-9602(14)60113-2
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