Question: For x* to be an interior minimum of f(x), it is necessary that 1. x* be a stationary point of f, that is, f(x*) =

For x* to be an interior minimum of f(x), it is necessary that
1. x* be a stationary point of f, that is, ∇f(x*) = 0, and
2. f be locally convex at x*, that is, Hf (x*) is nonnegative definite
If furthermore Hf(x*) is positive definite, then x* is a strict local minimum. The following result was used to prove the mean value theorem (exercise 4.34) in chapter 4.

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