supremum function

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

    Subdifferentials of nonconvex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data

  • Boris S. Mordukhovich
  • Nghia Tran
    • Categories Nonsmooth Optimization, Semi-infinite Programming Tags , , ,

    The paper is devoted to the subdifferential study and applications of the supremum of uniformly Lipschitzian functions over arbitrary index sets with no topology. Based on advanced techniques of variational analysis, we evaluate major subdifferentials of the supremum functions in the general framework of Asplund (in particular, reflexive) spaces with no convexity or relaxation assumptions. … Read more