On the minimum norm solution of linear programs

C. Kanzow, H. Qi, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

40 Citations (Scopus)

Abstract

This paper describes a new technique to find the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Newton-type method converges in a finite number of iterations to the minimum norm solution of the underlying linear program.
Original languageEnglish
Pages (from-to)333-345
Number of pages13
JournalJournal of Optimization Theory and Applications
Volume116
Issue number2
DOIs
Publication statusPublished - 1 Feb 2003

Keywords

  • finite termination
  • Linear programs
  • minimum norm solution
  • Newton method
  • unconstrained minimization

ASJC Scopus subject areas

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

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