Locally Lipschitz Gradient

Composite optimization models via proximal gradient method with a novel enhanced adaptive stepsize

  • Pham Thi Hoai
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We consider the {\it composite optimization problems} under convex and nonconvex settings. For the convex case, the {\it locally Lipschitz} condition is imposed on the gradient of the differentiable convex term. The classical {\it proximal gradient method} will be studied with our novel {\it enhanced adaptive} stepsize selection. To obtain the convergence of the proposed … Read more

    AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization

  • Danqing Zhou
  • Shiqian Ma
  • Junfeng Yang
    • Categories Convex Optimization Tags , , , , ,

    In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for general unconstrained convex optimization. We analyze the ergodic convergence of the objective function value and the convergence of the iterates for solving general … Read more