Two classes of merit functions for infinite-dimensional second order complimentary problems

Juhe Sun, Jein Shan Chen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.

Original languageEnglish
Pages (from-to)387-413
Number of pages27
JournalNumerical Functional Analysis and Optimization
Volume31
Issue number4
DOIs
Publication statusPublished - 2010 Apr 1

Fingerprint

Merit Function
Complementarity Problem
Nonlinear Complementarity Problem
Bounded Set
Class
Level Set
Unique Solution
Error Bounds

Keywords

  • Error bound
  • Fixed point
  • Hilbert space
  • Level set
  • Merit functions
  • Second-order cone

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this

Two classes of merit functions for infinite-dimensional second order complimentary problems. / Sun, Juhe; Chen, Jein Shan.

In: Numerical Functional Analysis and Optimization, Vol. 31, No. 4, 01.04.2010, p. 387-413.

Research output: Contribution to journalArticle

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