Globally and quadratically convergent algorithm for minimizing the sum of Euclidean norms

G. Zhou, K.C. Toh, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported.
Original languageEnglish
Pages (from-to)357-377
Number of pages21
JournalJournal of Optimization Theory and Applications
Volume119
Issue number2
DOIs
Publication statusPublished - 1 Nov 2003
Externally publishedYes

Keywords

  • Quadratic convergence
  • Strict complementarity
  • Sum of norms

ASJC Scopus subject areas

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

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