Unconstrained Optimization

Abstract

1. We say x ∈ X is a local maximum of f on X if there is r > 0 such that f(x) ≥ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local maximum. 2. We say x ∈ X is a local minimum of f on X if there is r > 0 such that f(x) ≤ f(y) for all y ∈ X ∩B(x, r). If the inequality is strict, then we have a strict local minimum. 3. We say x ∈ X is a global maximum of f on X if f(x) ≥ f(y) for all y ∈ X. If the inequality is strict, then we have a strict global maximum.