Unconstrained Optimization

N. Tutkun
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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.
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1. 如果对所有y∈x∩B(x, r)存在r > 0使得f(x)≥f(y),则x∈x是f在x上的一个局部极大值。如果不等式是严格的,则我们有一个严格的局部极大值。2. 如果对所有y∈x∩B(x, r)存在r > 0使得f(x)≤f(y),则x∈x是f在x上的一个局部极小值。如果不等式是严格的,则我们有一个严格的局部极小值。3.如果对于所有y∈x, f(x)≥f(y),则x∈x是f在x上的一个全局极大值。如果不等式是严格的,则我们有一个严格的全局极大值。
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