proximity operator

A Proximal Interior Point Algorithm with Applications to Image Processing

  • Émilie Chouzenoux
  • Marie-Caroline Corbineau
  • Jean-Christophe Pesquet
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying … Read more

    Deep Neural Network Structures Solving Variational Inequalities

  • Patrick L. Combettes
  • Jean-Christophe Pesquet
    • Categories Complementarity and Variational Inequalities, Convex Optimization Tags , , , ,

    We propose a novel theoretical framework to investigate deep neural networks using the formalism of proximal fixed point methods for solving variational inequalities. We first show that almost all activation functions used in neural networks are actually proximity operators. This leads to an algorithmic model alternating firmly nonexpansive and linear operators. We derive new results … Read more