Zigzag phenomenon

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Successive directions are orthogonal, causing Cauchy's steepest ascent   to converge  slowly. The successive orthogonality comes from optimizing the (scalar) step size with (exact) line search, but the issue runs deeper. In general, the zigzag phenomenon causes small steps around a ridge. See Wolfe's example, where zigzagging causes non-convergence; also see Myths and counter examples in mathematical programming.


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