Unified approaches to nonlinear optimization

Liang Ju Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number1
Publication statusPublished - 1999


  • 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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