Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Karush-Kuhn-Tucker and duality<br />
Remarks:<br />
Very general result, strong tool <strong>in</strong> convex optimization<br />
Dual problem simpler to solve, (yopt, zopt) called Kuhn Tucker po<strong>in</strong>t.<br />
The triple (xopt, yopt, zopt) exist if and only if it def<strong>in</strong>es a saddle po<strong>in</strong>t<br />
of the Lagrangian L <strong>in</strong> that<br />
L(xopt, y, z) ≤ L(xopt, yopt, zopt)<br />
<br />
for all x, y ≥ 0 and z.<br />
=Popt=Dopt<br />
≤ L(x, yopt, zopt)<br />
Siep Weiland and Carsten Scherer (DISC) <strong>L<strong>in</strong>ear</strong> <strong>Matrix</strong> <strong>Inequalities</strong> <strong>in</strong> <strong>Control</strong> Class 1 39 / 59
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