Hahn-Banach theorems and subgradients of set-valued maps

Jian Wen Peng; Heung Wing Joseph Lee; Wei Dong Rong; Xin Min Yang

doi:10.1007/s001860400397

Hahn-Banach theorems and subgradients of set-valued maps

Jian Wen Peng
, Heung Wing Joseph Lee
, Wei Dong Rong
, Xin Min Yang

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

10 Citations (Scopus)

Abstract

Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps.

Original language	English
Pages (from-to)	281-297
Number of pages	17
Journal	Mathematical Methods of Operations Research
Volume	61
Issue number	2
DOIs	https://doi.org/10.1007/s001860400397
Publication status	Published - 1 Jun 2005

Keywords

Hahn-Banach theorem
Lagrange multiplier theorem
Sandwich theorem
Set-Valued map
Subgradient

ASJC Scopus subject areas

Software
General Mathematics
Management Science and Operations Research

More information

10.1007/s001860400397

Cite this

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title = "Hahn-Banach theorems and subgradients of set-valued maps",

abstract = "Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps.",

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AU - Peng, Jian Wen

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AB - Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. We present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps.

KW - Hahn-Banach theorem

KW - Lagrange multiplier theorem

KW - Sandwich theorem

KW - Set-Valued map

KW - Subgradient

UR - https://www.scopus.com/pages/publications/18844428070

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DO - 10.1007/s001860400397

M3 - Journal article

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EP - 297

JO - Mathematical Methods of Operations Research

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IS - 2

ER -

Hahn-Banach theorems and subgradients of set-valued maps

Abstract

Keywords

ASJC Scopus subject areas

More information

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