broyden-fletcher-goldfarb-shanno (bfgs)

Non-asymptotic superlinear convergence of Nesterov accelerated BFGS

  • Manish Kumar Sahu
  • Suvendu Pattanaik
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This paper studies the convergence of a Nesterov accelerated variant of the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) quasi-Newton method in the setting where the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We demonstrate that similar to the classic BFGS method, the Nesterov accelerated BFGS method … Read more

    Limited-Memory BFGS with Displacement Aggregation

  • Albert S. Berahas
  • Frank E. Curtis
  • Baoyu Zhou
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS (a.k.a. L-BFGS) method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a full-memory BFGS method. This means that, if a sufficiently large number of pairs are stored, then an optimization algorithm employing … Read more