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Block BFGS Methods

Wenbo Gao (wg2279***at***columbia.edu)
Donald Goldfarb (goldfarb***at***ieor.columbia.edu)

Abstract: We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and discuss other modifications for non-convex minimization. Numerical experiments comparing Block BFGS, BFGS and gradient descent are presented.

Keywords: Unconstrained optimization, quasi-Newton methods, BFGS, block updates

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: manuscript, Dept. of Industrial Engineering and Operations Research, Columbia University, New York, NY, Sept 2016.

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Entry Submitted: 10/01/2016
Entry Accepted: 10/01/2016
Entry Last Modified: 12/05/2016

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