Pedro Pérez-Aros

Lipschitz Gradient Guarantees for Probability Functions and a New Algorithm for Probability Maximization

  • Wim van Ackooij
  • Carolina Chiu
  • Welington de Oliveira
  • Pedro Pérez-Aros
    • Categories Stochastic Programming Tags , , ,

    This work studies probability functions that appear in stochastic programming models. Although their differentiability has been widely investigated, the Lipschitz continuity of their gradients, crucial for the design and analysis of modern optimization algorithms, has received little attention. We develop a general framework that ensures differentiability and gradient Lipschitz continuity under practical conditions. Our framework … Read more

    Approximating inequality systems within probability functions: studying implications for problems and consistency of first-order information

  • Wim van Ackooij
  • Pedro Pérez-Aros
  • David Villacís
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , , ,

    In this work, we are concerned with the study of optimization problems featuring so-called probability or chance constraints. Probability constraints measure the level of satisfaction of an underlying random inequality system and ensure that this level is high enough. Such an underlying inequality system could be expressed by an abstractly known or perhaps costly to … Read more

    A Variational Analysis Approach for Bilevel Hyperparameter Optimization with Sparse Regularization

  • David Villacís
  • Pedro Pérez-Aros
  • Emilio Vilches
    • Categories Bilevel Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , , ,

    We study a bilevel optimization framework for hyperparameter learning in variational models, with a focus on sparse regression and classification tasks. In particular, we consider a weighted elastic-net regularizer, where feature-wise regularization parameters are learned through a bilevel formulation. A key novelty of our approach is the use of a Forward-Backward (FB) reformulation of the … Read more

    Moreau envelope of supremum functions with applications to infinite and stochastic programming

  • Pedro Pérez-Aros
  • Emilio Vilches
    • Categories Convex Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    In this paper, we investigate the Moreau envelope of the supremum of a family of convex, proper, and lower semicontinuous functions. Under mild assumptions, we prove that the Moreau envelope of a supremum is the supremum of Moreau envelopes, which allows us to approximate possibly nonsmooth supremum functions by smooth functions that are also the … Read more