Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
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Example<br />
2<br />
• exact signal ˆx ∈ R 1000<br />
• 10 nonzero components<br />
ˆxk<br />
1<br />
0<br />
−1<br />
−2<br />
0 200 400 600 800 1000<br />
k<br />
least-norm solutions (randomly generated A ∈ R 100×1000 )<br />
minimum l 2 -norm solution<br />
minimum l 1 -norm solution<br />
2<br />
2<br />
1<br />
1<br />
xk<br />
0<br />
xk<br />
0<br />
−1<br />
−1<br />
−2<br />
0 200 400 600 800 1000<br />
k<br />
−2<br />
0 200 400 600 800 1000<br />
k<br />
l 1 -norm estimate is exact<br />
<strong>Piecewise</strong>-<strong>linear</strong> <strong>optimization</strong> 2–14
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