Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Duality and convex programs<br />
Some term<strong>in</strong>ology:<br />
Remarks:<br />
Lagrange function: L(x, y, z)<br />
Lagrange dual cost: ℓ(y, z)<br />
Lagrange dual optimization problem:<br />
Dopt := sup ℓ(y, z)<br />
y≥0, z<br />
ℓ(y, z) computed by solv<strong>in</strong>g an unconstra<strong>in</strong>ed optimization problem.<br />
Is concave function.<br />
Dual problem is concave maximization problem. Constra<strong>in</strong>ts are<br />
simpler than <strong>in</strong> primal problem<br />
Ma<strong>in</strong> question: when is Dopt = Popt?<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 35 / 59
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