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Local Minimum


Given
x ∈ Rn

x is a local minimum if

∃ r > 0 : ∀ y ∈ Br(x) => f(x) ≤ f(y)

Note1: Similarly we can define the strict local minimum if the inequality we substitute f(x) < f(y)
Note2: Similarly we define the local maximum if we substitute the inequality less-equal to greater-equal.