weakly convex

Minimizing the difference of convex and weakly convex functions via bundle method

  • Ksenia Syrtseva
  • Welington de Oliveira
  • Sophie Demassey
  • Wim van Ackooij
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We consider optimization problems with objective and constraint being the difference of convex and weakly convex functions. This framework covers a vast family of nonsmooth and nonconvex optimization problems, particularly those involving Difference-of-Convex (DC) functions with known DC decomposition, functions whose gradient is Lipschitz continuous, as well as problems that comprise certain classes of composite … Read more

    Stochastic model-based minimization of weakly convex functions

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    We consider an algorithm that successively samples and minimizes stochastic models of the objective function. We show that under weak-convexity and Lipschitz conditions, the algorithm drives the expected norm of the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. Our result yields the first complexity guarantees for the stochastic proximal point algorithm … Read more