A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Applications of smoothing methods in numerical analysis and optimization
Focus on computational neurobiology
Hedging with a correlated asset: Solution of a nonlinear pricing PDE
Journal of Computational and Applied Mathematics
A smoothing Newton-type method for generalized nonlinear complementarity problem
Journal of Computational and Applied Mathematics
An entropy regularization technique for minimizing a sum of Tchebycheff norms
Applied Numerical Mathematics
Journal of Global Optimization
Computational Optimization and Applications
On the convergence of a modified algorithm for the spherical facility location problem
Operations Research Letters
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We consider the problem of minimizing a sum of Euclidean norms, $f(x) = \sum_{i=1}^m\|b_i - A_i^Tx \|$. This problem is a nonsmooth problem because f is not differentiable at a point x when one of the norms is zero. In this paper we present a smoothing Newton method for this problem by applying the smoothing Newton method proposed by Qi, Sun, and Zhou [Math. Programming, 87 (2000), pp. 1--35] directly to a system of strongly semismooth equations derived from primal and dual feasibility and a complementarity condition. This method is globally and quadratically convergent. As applications to this problem, smoothing Newton methods are presented for the Euclidean facilities location problem and the Steiner minimal tree problem under a given topology. Preliminary numerical results indicate that this method is extremely promising.