Unified approaches to nonlinear optimization

Liang Ju Chu

doi:10.1080/02331939908844443

Unified approaches to nonlinear optimization

Liang Ju Chu^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking of convex-valued multifunctions to acyclic multifunctions and the relaxation of the compactness condition on constraint regions. The aim of this paper is to develop as consequences of fixed point theory a variety of existence results relevant to coincidence theorems, generalized KKM type theorems and some unified variational inequalities including quasi-variational inequalities without monotonicity nor metrizability.

Original language	English
Pages (from-to)	25-60
Number of pages	36
Journal	Optimization
Volume	46
Issue number	1
DOIs	https://doi.org/10.1080/02331939908844443
Publication status	Published - 1999

Keywords

Acyclic multifunction
Coincidence
Complementarity problem
Convex programming
Convex space
Fan's matching theorem
Fixed point
KKM mapping
KKM theorem
Karamardian condition
Partition of unity
Quasi-variational inequality
Variational inequality

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1080/02331939908844443

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title = "Unified approaches to nonlinear optimization",

abstract = "This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking of convex-valued multifunctions to acyclic multifunctions and the relaxation of the compactness condition on constraint regions. The aim of this paper is to develop as consequences of fixed point theory a variety of existence results relevant to coincidence theorems, generalized KKM type theorems and some unified variational inequalities including quasi-variational inequalities without monotonicity nor metrizability.",

keywords = "Acyclic multifunction, Coincidence, Complementarity problem, Convex programming, Convex space, Fan's matching theorem, Fixed point, KKM mapping, KKM theorem, Karamardian condition, Partition of unity, Quasi-variational inequality, Variational inequality",

author = "Chu, {Liang Ju}",

note = "Funding Information: *This work is partially supported by the National Science Council of the Republic of China under the grant NSC 87-21 15-M003-005.",

year = "1999",

doi = "10.1080/02331939908844443",

language = "English",

volume = "46",

pages = "25--60",

journal = "Optimization",

issn = "0233-1934",

publisher = "Taylor and Francis Ltd.",

number = "1",

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TY - JOUR

T1 - Unified approaches to nonlinear optimization

AU - Chu, Liang Ju

N1 - Funding Information: *This work is partially supported by the National Science Council of the Republic of China under the grant NSC 87-21 15-M003-005.

PY - 1999

Y1 - 1999

N2 - This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking of convex-valued multifunctions to acyclic multifunctions and the relaxation of the compactness condition on constraint regions. The aim of this paper is to develop as consequences of fixed point theory a variety of existence results relevant to coincidence theorems, generalized KKM type theorems and some unified variational inequalities including quasi-variational inequalities without monotonicity nor metrizability.

AB - This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking of convex-valued multifunctions to acyclic multifunctions and the relaxation of the compactness condition on constraint regions. The aim of this paper is to develop as consequences of fixed point theory a variety of existence results relevant to coincidence theorems, generalized KKM type theorems and some unified variational inequalities including quasi-variational inequalities without monotonicity nor metrizability.

KW - Acyclic multifunction

KW - Coincidence

KW - Complementarity problem

KW - Convex programming

KW - Convex space

KW - Fan's matching theorem

KW - Fixed point

KW - KKM mapping

KW - KKM theorem

KW - Karamardian condition

KW - Partition of unity

KW - Quasi-variational inequality

KW - Variational inequality

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U2 - 10.1080/02331939908844443

DO - 10.1080/02331939908844443

M3 - Article

AN - SCOPUS:26444588204

SN - 0233-1934

VL - 46

SP - 25

EP - 60

JO - Optimization

JF - Optimization

IS - 1

ER -

Unified approaches to nonlinear optimization

Abstract

Keywords

ASJC Scopus subject areas

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