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. © 2002 Elsevier Science B.V. All rights reserved.
Qi, L., Sun, D., & Zhou, G. (2002). A primal-dual algorithm for minimizing a sum of Euclidean norms. Journal of Computational and Applied Mathematics, 138(1), 127–150. https://doi.org/10.1016/S0377-0427(01)00357-0