Conic positive definiteness and sharp minima of fractional orders in vector optimization problems

Xi Yin Zheng; Xiaoqi Yang

doi:10.1016/j.jmaa.2012.02.045

Conic positive definiteness and sharp minima of fractional orders in vector optimization problems

Xi Yin Zheng, Xiaoqi Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

4 Citations (Scopus)

Abstract

Motivated by the fact that the usual positive definiteness does not work in an infinite space, we introduce the concept of S-positive definiteness with respect to an ordering cone in a general Banach space and show that the S-positive definiteness plays the same role as the usual positive definiteness in the finite dimensional case. As applications, we study sharp and weak sharp minima of fractional orders in vector optimization.

Original language	English
Pages (from-to)	619-629
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	391
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.02.045
Publication status	Published - 15 Jul 2012

Keywords

Conic positive definiteness
Ideal solution
Pareto solution
Sharp minima
Weak Pareto solution

ASJC Scopus subject areas

Analysis
Applied Mathematics

More information

10.1016/j.jmaa.2012.02.045

Cite this

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abstract = "Motivated by the fact that the usual positive definiteness does not work in an infinite space, we introduce the concept of S-positive definiteness with respect to an ordering cone in a general Banach space and show that the S-positive definiteness plays the same role as the usual positive definiteness in the finite dimensional case. As applications, we study sharp and weak sharp minima of fractional orders in vector optimization.",

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AU - Yang, Xiaoqi

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N2 - Motivated by the fact that the usual positive definiteness does not work in an infinite space, we introduce the concept of S-positive definiteness with respect to an ordering cone in a general Banach space and show that the S-positive definiteness plays the same role as the usual positive definiteness in the finite dimensional case. As applications, we study sharp and weak sharp minima of fractional orders in vector optimization.

AB - Motivated by the fact that the usual positive definiteness does not work in an infinite space, we introduce the concept of S-positive definiteness with respect to an ordering cone in a general Banach space and show that the S-positive definiteness plays the same role as the usual positive definiteness in the finite dimensional case. As applications, we study sharp and weak sharp minima of fractional orders in vector optimization.

KW - Conic positive definiteness

KW - Ideal solution

KW - Pareto solution

KW - Sharp minima

KW - Weak Pareto solution

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DO - 10.1016/j.jmaa.2012.02.045

M3 - Journal article

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Conic positive definiteness and sharp minima of fractional orders in vector optimization problems

Abstract

Keywords

ASJC Scopus subject areas

More information

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