On Minimizing the Maximum Eigenvalue of a Symmetric Matrix
On Minimizing the Maximum Eigenvalue of a Symmetric Matrix
An important optimization problem that arises in control is to minimize $\varphi ( x )$, the largest eigenvalue (in magnitude) of a symmetric matrix function of x. If the matrix function is affine, $\varphi ( x )$ is convex. However, $\varphi ( x )$ is not differentiable, since the eigenvalues …