lyapunov function

Stochastic subgradient method converges on tame functions

  • Damek Davis
  • Dmitriy Drusvyatskiy
  • Jason D. Lee
  • Sham Kakade
    • Categories Nonsmooth Optimization Tags , , , ,

    This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz function, produces limit points that are all first-order stationary. More generally, our result applies to any function with a Whitney stratifiable graph. … Read more

    Linear Convergence of Proximal Incremental Aggregated Gradient Methods under Quadratic Growth Condition

  • Hui Zhang
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a non-smooth convex function. In this paper, under the quadratic growth condition{a strictly weaker condition than the strongly convex assumption, … Read more