A primal-dual algorithm for minimizing a sum of Euclidean norms

Liqun Qi, Defeng Sun, Guanglu Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


We study the problem of minimizing a sum of Euclidean norms. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. In this paper we first transform this problem and its dual problem into a system of strongly semismooth equations, and give some uniqueness theorems for this problem. We then present a primal-dual algorithm for this problem by solving this system of strongly semismooth equations. Preliminary numerical results are reported, which show that this primal-dual algorithm is very promising.
Original languageEnglish
Pages (from-to)127-150
Number of pages24
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 1 Jan 2002


  • Euclidean facilities location
  • Prima-dual algorithm
  • Semismooth
  • Steiner minimum trees
  • Sum of norms
  • VLSL design

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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