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

Authors:
Liqun Qi;Defeng Sun;Guanglu Zhou
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China;Department of Mathematics, National University of Singapore, Singapore;Department of Mathematics, National University of Singapore, Singapore
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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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.