A primal–dual algorithm for minimizing a sum of Euclidean norms
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摘要
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.
论文关键词:90C33,90C30,65H10,Primal–dual algorithm,Sum of norms,Semismooth,VLSL design,Euclidean facilities location,Steiner minimum trees
论文评审过程:Received 28 February 2000, Revised 24 November 2000, Available online 29 October 2001.
论文官网地址:https://doi.org/10.1016/S0377-0427(01)00357-0