The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. We derive a primal-dual interior-point algorithm for the problem, by applying Newton’s method directly to a system of nonlinear e...

In this note we study contractivity of monotone systems and exponential convergence positive using non-Euclidean norms. We first introduce the notion conic matrix measure as a framework to stability systems. properties measures investigate their connection with weak pairings standard measures. Using pairings, characterize incremental respect Moreover, use provide sufficient conditions for equil...

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these are graph-based: they associate vertex each point weighted edge pair. Existing theory shows that the Laplacian matrix graph converges to Laplace–Beltrami operator manifold, under assumption pairwise affinities...

In applying clustering to multivariate data, in which there are some largescale variables, clustering results depend on the variables more than the user’s needs. In such cases, we should standardize the data to control the dependency. For high-dimensional data, Doherty et al. (Appl Soft Comput 7:203–210, 2007) argued numerically that data standardization by variable range leads to almost the sa...

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

A comparison of different T-norms and S-norms for interval type-2 fuzzy number weights is proposed in this work. The interval type-2 fuzzy number weights are used in a neural network with an interval backpropagation learning enhanced method for weight adjustment. Results of experiments and a comparative research between traditional neural networks and the neural network with interval type-2 fuz...

We propose a novel technique for direct visual matching of images for the purposes of face recognition and database search. Specifically, we argue in favor of a probabilistic measure of similarity, in contrast to simpler methods which are based on standard Euclidean L2 norms (template matching) or subspace-restricted norms (eigenspace matching). The proposed similarity measure is based on a Bay...

Abstract In this paper, we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The functionals double integrals, equivalent to semi-norms the Euclidean setting. extend analysis [14] concerning...