Unified approaches to nonlinear optimization

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)25-60
Number of pages36
JournalOptimization
Volume46
Issue number1
DOIs
Publication statusPublished - 1999 Jan 1

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Vector spaces
Nonlinear Optimization
Coincidence Theorem
Metrizability
Quasi-variational Inequalities
Fixed Point Theory
Topological Vector Space
Variational Inequalities
Existence Results
Compactness
Monotonicity
Nonlinear Problem
Optimization Problem
Theorem
Nonlinear optimization
Optimization problem
Fixed point
Quasi-variational inequalities
Variational inequalities

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

Cite this

Unified approaches to nonlinear optimization. / Chu, Liang-Ju.

In: Optimization, Vol. 46, No. 1, 01.01.1999, p. 25-60.

Research output: Contribution to journalArticle

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