Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
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Linear and affine functions<br />
<strong>linear</strong> function: a function f : R n → R is <strong>linear</strong> if<br />
f(αx+βy) = αf(x)+βf(y)<br />
∀x,y ∈ R n ,α,β ∈ R<br />
property: f is <strong>linear</strong> if and only if f(x) = a T x for some a<br />
affine function: a function f : R n → R is affine if<br />
f(αx+(1−α)y) = αf(x)+(1−α)f(y)<br />
∀x,y ∈ R n ,α ∈ R<br />
property: f is affine if and only if f(x) = a T x+b for some a, b<br />
<strong>Piecewise</strong>-<strong>linear</strong> <strong>optimization</strong> 2–2
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