prox-regular functions

Second-order growth, tilt stability, and metric regularity of the subdifferential

  • Dmitriy Drusvyatskiy
  • Boris S. Mordukhovich
  • Nghia Tran
    • Categories Nonsmooth Optimization Tags , , , , ,

    This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive definiteness/semidefiniteness properties of the second-order subdifferential (or generalized … Read more

    A proximal method for composite minimization

  • Adrian Lewis
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions … Read more