Convergence theorems for lp-norm minimizers with respect to p

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let C be a fixed compact convex subset of ℝ++ and let x p be the unique minimal lp-norm element in C for any p: \ 1<p<\∞. In this paper, we study the convergence of x p as p→ ∞ or p ↘ 1, respectively. We characterize also the limit point as the minimal element of C with respect to the lexical minimax order relation or the lexical minitotal order relation, respectively.

Original languageEnglish
Pages (from-to)577-589
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume125
Issue number3
DOIs
Publication statusPublished - 2005 Jun

Fingerprint

Order Relation
Lp-norm
Minimizer
Convergence Theorem
Limit Point
Minimax
Subset

Keywords

  • Approximations
  • l-norm
  • Lexicographical orders
  • Minimum-norm problems

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

Cite this

Convergence theorems for lp-norm minimizers with respect to p. / Kido, Kazuo.

In: Journal of Optimization Theory and Applications, Vol. 125, No. 3, 06.2005, p. 577-589.

Research output: Contribution to journalArticle

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