Taylor expansion

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For LaTeX: \textstyle f \in C^n, Taylor's Theorem is used by dropping the remainder term. The first-order expansion is LaTeX: \textstyle f(x) = f(y) + \nabla f(x) * (x-y), and the second-order expansion is

LaTeX: \textstyle f(x) = f(y) + \nabla f(x) * (x-y) + \frac{1}{2}\, (x-y)' H_{f(x)} * (x-y).

(See Myths and Counter Examples in Mathematical Programming to avoid misconception.)


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