block mirror descent

Block Majorization Minimization with Extrapolation and Application to $\beta$-NMF

  • Le Thi Khanh Hien
  • Valentin Leplat
  • Nicolas Gillis
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

    We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that block majorization minimization can be reformulated as a block mirror descent method, with the Bregman divergence adaptively updated at each iteration, … Read more

    Block Coordinate Descent Almost Surely Converges to a Stationary Point Satisfying the Second-order Necessary Condition

  • Zhubin Shen
  • Qingjiang Shi
  • Enbin Song
    • Categories Unconstrained Optimization Tags , , , , ,

    Given a non-convex twice continuously differentiable cost function with Lipschitz continuous gradient, we prove that all of the block coordinate gradient descent, block mirror descent and proximal block coordinate descent methods converge to stationary points satisfying the second-order necessary condition, almost surely with random initialization. All our results are ascribed to the center-stable manifold theorem … Read more