Smoothing Newton method for minimizing the sum of \(p\) -norms
type: Item
instance of: scholarly article
title: Smoothing Newton method for minimizing the sum of \(p\) -norms
zbMATH Open document ID: 1153.90022
author: B. E. Eshmatov
published in: Journal of Optimization Theory and Applications
publication date: 2008-09-22T00:00:00Z
review text: This paper considers the problem of minimizing the sum of \(p\)-norms, where \(p\) is a fixed real number in the interval \( [1,2]\). This nondifferentiable problem arises in many applications, including the very-large-scale-integration layout problem, the facilities location problem and the Steiner minimum tree problem under a given topology. The authors establish the optimality conditions, duality and uniqueness results for the problem, and then proposed a smoothing Newton method for the problem with \(p\in [1,2]\) based on the semismooth equations derived from the optimality conditions. The method is globally and superlinearly convergent, and furthemore it is quadratically convergent when \(p\in [1,3/2] \cup\{2\}\). In particular, the quadratic convergence for \(p\in [1,3/2] \cup\{2\}\) is proved without requiring strict complementarity. Numerical experiments confirm the good theoretical properties of the method.
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 5345658
zbMATH Keywords: sum of \(p\)-norms
zbMATH Keywords: semismoothness
zbMATH Keywords: smoothing Newton method
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: s10957-008-9364-8
OpenAlex ID: W1976785066
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DOI: 10.1007/S10957-008-9364-8
description: scientific article; zbMATH DE number 5345658