  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.
