Convex numerical radius

Galán, M. Ruiz

doi:10.1016/j.jmaa.2009.07.037

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Cited by 3 publications

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“…Proof. It follows from the well-known Brønsted-Rockafellar theorem that ∂g(R n ) is dense in R n ; see [22,Theorem 2.3]. We first show that the set ∂g(R n ) is closed.…”

Section: Algorithmmentioning

confidence: 90%

Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering

Nam

Rector

Giles

2017

J Optim Theory Appl

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In this paper we develop algorithms to solve generalized Fermat-Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.

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“…Proof. It follows from the well-known Brønsted-Rockafellar theorem that ∂g(R n ) is dense in R n ; see [22,Theorem 2.3]. We first show that the set ∂g(R n ) is closed.…”

Section: Algorithmmentioning

confidence: 90%