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Show that the symmetric rank-one update 2 18 and the BFGS update 2 19 are scale-invariant if the initial Hessian approximations B0 are chosen appropriately That is using the notation of the

Show that the symmetric rank-one update (2.18) and the BFGS update (2.19) are scale-invariant if the initial Hessian approximations B0 are chosen appropriately. That is, using the notation of the previous exercise, show that if these methods are applied to f (x) starting from x0 Sz0 + s with initial Hessian B0, and to ˜f (z) starting from z0 with initial Hessian ST B0S, then all iterates are related by xk =Szk + s. (Assume for simplicity that the methods take unit step lengths.)

Aug 06 2020 View more View Less

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