The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations

Abstract EN

We study optimization problems involving eigenvalues of symmetricmatrices.

We present a nonsmooth optimization technique for a class of nonsmooth functions whichare semi-infinite maxima of eigenvalue functions.

Our strategy uses generalized gradients and ? ? space decomposition techniques suited for the norm and other nonsmooth performance criteria.

Forthe class of max-functions, which possesses the so-called primal-dual gradient structure, we computesmooth trajectories along which certain second-order expansions can be obtained.

We also give thefirst- and second-order derivatives of primal-dual function in the space of decision variables R m undersome assumptions.