Newton’s Method for Unconstrained Optimization

Step 3 Set xk+1 ← xk + αk dk,k← k +1.Goto Step 1 . Note the following: • The method assumes H(xk) is nonsingular at each iteration. • There is no guarantee that f(xk+1) ≤ f(x k ). • Step 2 could be augmented by a line-search of f(xk + αdk)tofind an optimal value of the step-size parameter α. Recall that we call a matrix SPD if it is symmetric and positive definite. ................
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