A Characterization of Properly Minimal Elements of a Set

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1985 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control and Optimization, volume 23, pages 649-656 (issn: 0363-0129, eissn: 1095-7138,

Copyright policy )

Authors: Jahn, Johannes;

doi: 10.1137/0323041

A Characterization of Properly Minimal Elements of a Set

- Summary
- Subjects
- Metrics

Abstract

The notion of properly minimal elements plays an important role in vector optimization. This paper characterizes the properly minimal elements of an arbitrary set in a real normal space with a partial ordering (induced by a convex cone) by the minimal solution of an appropriate approximation problem without any convexity assumption. The necessary and sufficient conditions for properly minimal elements are presented. The importance of approximation theory in vector optimization is formulated.

Keywords

scalarization, vector optimization, real normal space, Sensitivity, stability, parametric optimization, properly minimal elements, approximation

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	32
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%