Results 251 to 260 of about 427,912 (276)

A Smoothing Newton Method for Minimizing a Sum of Euclidean Norms

SIAM Journal on Optimization, 2000
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 [
Liqun Qi, Guanglu Zhou
exaly   +4 more sources

Euclidean Domains With No Multiplicative Norms

Communications in Algebra
We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to $\mathbb{R}$ (under its usual order). A key step in the proof is showing that the UFD property is preserved when adjoining a free factorization.
Dastrup, Caleb J., Nielsen, Pace P.
exaly   +3 more sources

Linear combination of norms in improving approximation of Euclidean norm

Pattern Recognition Letters, 2013
In the past, different distance functions and their combinations had been proposed as good approximators of Euclidean metrics. In particular in recent years, a few distance functions with their general forms in n-dimensional real and integer spaces were identified for their improved performances in approximating corresponding Euclidean metrics. In this
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Euclidean Sections of Direct Sums of Normed Spaces

Canadian Mathematical Bulletin, 2003
AbstractWe study the dimension of “random” Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from [LMS], to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much “weaker” randomness of “diagonal” subspaces (Corollary 1.4 and explanation ...
Litvak, A. E., Milman, V. D.
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The Minimal Euclidean Norm of an Algebraic Number Is Effectively Computable

Journal of Algorithms, 1994
For a polynomial \(P(x)= p_ 0+\dots +p_ n x^ n\), the Euclidean norm \(\| P\|\), defined to be the Euclidean norm of the vector \((p_ 0,\dots, p_ n)\). The minimal Euclidean norm \(\| \alpha\|_{\min}\) of an algebraic number \(\alpha\) is defined to be the minimum of \(\| P\|\) over all polynomials with integer coefficients for which \(P(\alpha)=0 ...
Michael Filaseta, M. L. Robinson, Ferrell S. Wheeler   +2 more
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A simple geometry of Euclidean norms

IEEE Transactions on Education, 1988
A simple two-dimensional geometry is presented for the Euclidean norm of a vector with any number of components. The proposed geometrical construction is an n-sided right triangle whose sides are the component elements of the vector. >
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An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications

SIAM Journal on Optimization, 1997
In recent years rich theories on polynomial-time interior-point algorithms have been developed. These theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications. In this paper, the problem of minimizing a sum of Euclidean norms is studied.
Guoliang Xue, Yinyu Ye 0001
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A quadratically convergent method for minimizing a sum of euclidean norms

Mathematical Programming, 1983
The author considers the problem of minimizing a sum of Euclidean norms \[ F(x)=\sum^{m}_{i=1}r_i(x) \] where the residuals \(r_i(x)\) are affine functions from \(R^n\) to \(R^l\) (\(n\geq l\geq 2,\quad m\geq 2)\). This arises in a number of applications, including single- and multi-facility location problems.
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Normativity of the Euclidean Ideal

2021
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Truncation of Small Matrix Elements Based on the Euclidean Norm for Blocked Data Structures

Journal of Computational Chemistry, 2009
Emanuel H Rubensson, Elias Rudberg, Paweł Sałek   +2 more
exaly