Warren Hare

Prox-Regularity and Stability of the Proximal Mapping

  • Warren Hare
  • R. A. Poliquin
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Robust Optimization Tags , , , ,

    Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective … Read more

    Computing Proximal Points on Nonconvex Functions

  • Warren Hare
  • Claudia Sagastizábal
    • Categories Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , ,

    The proximal point mapping is the basis of many optimization techniques for convex functions. By means of variational analysis, the concept of proximal mapping was recently extended to nonconvex functions that are prox-regular and prox-bounded. In such a setting, the proximal point mapping is locally Lipschitz continuous and its set of fixed points coincide with … Read more