Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
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• equivalent LP in matrix notation<br />
minimize ˜c T˜x<br />
subject to Øx ≤˜b<br />
with<br />
˜x =<br />
⎡<br />
⎣ x ⎤<br />
t 1<br />
⎦, ˜c =<br />
t 2<br />
⎡<br />
⎣ 0 1<br />
1<br />
⎤<br />
⎦, Ã =<br />
⎡<br />
⎢<br />
⎣<br />
a T 1 −1 0<br />
. . .<br />
a T m −1 0<br />
c T 1 0 −1<br />
. . .<br />
0 −1<br />
c T p<br />
⎤ ⎡<br />
, ˜b = ⎥ ⎢<br />
⎦ ⎣<br />
⎤<br />
−b 1<br />
.<br />
−b m<br />
−d 1<br />
⎥<br />
. ⎦<br />
−d p<br />
<strong>Piecewise</strong>-<strong>linear</strong> <strong>optimization</strong> 2–6
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