The Experts below are selected from a list of 1662 Experts worldwide ranked by ideXlab platform

Ph. Tchamitchian - One of the best experts on this subject based on the ideXlab platform.

  • pointwise analysis of riemann s Nondifferentiable Function
    Inventiones Mathematicae, 1991
    Co-Authors: M. Holschneider, Ph. Tchamitchian
    Abstract:

    We will show how to analyse the local regularity of Functions with the help of the wavelet transform. These results will be applied to the Function of Riemann, where we show the existence of a dense set of points where this Function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the Functions will be shown to be not differentiable.

  • Pointwise analysis of Riemann's “Nondifferentiable” Function
    Inventiones Mathematicae, 1991
    Co-Authors: M. Holschneider, Ph. Tchamitchian
    Abstract:

    We will show how to analyse the local regularity of Functions with the help of the wavelet transform. These results will be applied to the Function of Riemann, where we show the existence of a dense set of points where this Function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the Functions will be shown to be not differentiable.

M. Holschneider - One of the best experts on this subject based on the ideXlab platform.

  • pointwise analysis of riemann s Nondifferentiable Function
    Inventiones Mathematicae, 1991
    Co-Authors: M. Holschneider, Ph. Tchamitchian
    Abstract:

    We will show how to analyse the local regularity of Functions with the help of the wavelet transform. These results will be applied to the Function of Riemann, where we show the existence of a dense set of points where this Function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the Functions will be shown to be not differentiable.

  • Pointwise analysis of Riemann's “Nondifferentiable” Function
    Inventiones Mathematicae, 1991
    Co-Authors: M. Holschneider, Ph. Tchamitchian
    Abstract:

    We will show how to analyse the local regularity of Functions with the help of the wavelet transform. These results will be applied to the Function of Riemann, where we show the existence of a dense set of points where this Function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the Functions will be shown to be not differentiable.

Prato Marco - One of the best experts on this subject based on the ideXlab platform.

  • Variable metric inexact line-search-based methods for nonsmooth optimization
    'Society for Industrial & Applied Mathematics (SIAM)', 2016
    Co-Authors: Bonettini Silvia, Loris Ignace, Porta Federica, Prato Marco
    Abstract:

    We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, Function plus a convex, possibly Nondifferentiable, Function. The key features of the proposed method are the definition of a suitable descent direction, based on the proximal operator associated to the convex part of the objective Function, and an Armijo-like rule to determine the stepsize along this direction ensuring the sufficient decrease of the objective Function. In this frame, we especially address the possibility of adopting a metric which may change at each iteration and an inexact computation of the proximal point defining the descent direction. For the more general nonconvex case, we prove that all limit points of the iterates sequence are stationary, while for convex objective Functions we prove the convergence of the whole sequence to a minimizer, under the assumption that a minimizer exists. In the latter case, assuming also that the gradient of the smooth part of the objective Function is Lipschitz, we also give a convergence rate estimate, showing the ${\mathcal O}(\frac 1 k)$ complexity with respect to the Function values. We also discuss verifiable sufficient conditions for the inexact proximal point and present the results of two numerical tests on total-variation-based image restoration problems, showing that the proposed approach is competitive with other state-of-the-art methods

Marco Prato - One of the best experts on this subject based on the ideXlab platform.

  • Variable metric inexact line-search based methods for nonsmooth optimization
    SIAM Journal on Optimization, 2016
    Co-Authors: Silvia Bonettini, Ignace Loris, Federica Porta, Marco Prato
    Abstract:

    We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, Function plus a convex, possibly Nondifferentiable, Function. The key features of the proposed method are the definition of a suitable descent direction, based on the proximal operator associated to the convex part of the objective Function, and an Armijo-like rule to determine the stepsize along this direction ensuring the sufficient decrease of the objective Function. In this frame, we especially address the possibility of adopting a metric which may change at each iteration and an inexact computation of the proximal point defining the descent direction. For the more general nonconvex case, we prove that all limit points of the iterates sequence are stationary, while for convex objective Functions we prove the convergence of the whole sequence to a minimizer, under the assumption that a minimizer exists. In the latter case, assuming also that the gradient of the smooth part of the objective Function...

Gutierrez Marcantoni, Luis Felipe - One of the best experts on this subject based on the ideXlab platform.

  • Nonuniform reinjection probability density Function in type V intermittency
    'Springer Science and Business Media LLC', 2018
    Co-Authors: Elaskar, Sergio Amado, Río, Ezequiel Del(ext), Gutierrez Marcantoni, Luis Felipe
    Abstract:

    In this paper, type V intermittency is studied using the M Function methodology developed in the last years. This methodology is applied on two different maps to evaluate the reinjection probability density Function (RPD), the probability density of laminar lengths and the characteristic relation. We have found that the RPD can be written as an exponential Function, where the uniform reinjection is only a singular case. Also, the probability density of laminar lengths can be a Nondifferentiable Function when the local map has a Nondifferentiable point inside the laminar interval. On the other hand, the characteristic relation is not unique, and it depends on the local map. Therefore, the behavior of the reinjection processes and the statistical properties for type V intermittency is wider than the previous studies have described. Finally, it is noted that the M Function methodology is a suitable tool to analyze type V intermittency.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: Río, Ezequiel del(EXT). Universidad Politécnica de Madrid; EspañaFil: Gutierrez Marcantoni, Luis Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentin

  • Non-uniform reinjection probability density Function in type V intermittency
    'Springer Science and Business Media LLC', 2018
    Co-Authors: Elaskar, Sergio Amado, Del Rio Ezequiel, Gutierrez Marcantoni, Luis Felipe
    Abstract:

    In this paper, type V intermittency is studied using the M Function methodology developed in the last years. This methodology is applied on two different maps to evaluate the reinjection probability density Function (RPD), the probability density of laminar lengths and the characteristic relation. We have found that the RPD can be written as an exponential Function, where the uniform reinjection is only a singular case. Also, the probability density of laminar lengths can be a Nondifferentiable Function when the local map has a Nondifferentiable point inside the laminar interval. On the other hand, the characteristic relation is not unique, and it depends on the local map. Therefore, the behavior of the reinjection processes and the statistical properties for type V intermittency is wider than the previous studies have described. Finally, it is noted that the M Function methodology is a suitable tool to analyze type V intermittency.Fil: Elaskar, Sergio Amado. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; ArgentinaFil: del Rio, Ezequiel. Universidad Politécnica de Madrid; EspañaFil: Gutierrez Marcantoni, Luis Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Estudios Avanzados en Ingeniería y Tecnología. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Estudios Avanzados en Ingeniería y Tecnología; Argentin