infinite programming

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

    Solving Infinite-dimensional Optimization Problems by Polynomial Approximation

  • Olivier Devolder
  • François Glineur
  • Yurii Nesterov
    • Categories Convex Optimization, Infinite Dimensional Optimization Tags , , , , , ,

    We solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional space and solve the corresponding finite-dimensional problems in a efficient way using structured convex optimization techniques. We prove … Read more