broyden-fletcher-goldfarb-shanno (bfgs)

Non-asymptotic superlinear convergence of Nesterov accelerated BFGS

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

    In this paper, we derive the explicit finite time local convergence of Nesterov accelerated the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) under the assumption that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We have shown that the rate of convergence of the NA-BFGS method is … 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