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

Liqun Qi; Defeng Sun; Guanglu Zhou

doi:10.1016/S0377-0427(01)00357-0

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

Liqun Qi, Defeng Sun, Guanglu Zhou

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	127-150
Number of pages	24
Journal	Journal of Computational and Applied Mathematics
Volume	138
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(01)00357-0
Publication status	Published - 1 Jan 2002

Keywords

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

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/S0377-0427(01)00357-0

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title = "A primal-dual algorithm for minimizing a sum of Euclidean norms",

abstract = "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.",

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AU - Sun, Defeng

AU - Zhou, Guanglu

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N2 - 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.

AB - 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.

KW - Euclidean facilities location

KW - Prima-dual algorithm

KW - Semismooth

KW - Steiner minimum trees

KW - Sum of norms

KW - VLSL design

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EP - 150

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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