We study optimization problems involving eigenvalues of symmetric matrices. We present a nonsmooth optimization technique for a class of nonsmooth functions which are semi-infinite maxima of eigenvalue functions. Our strategy uses generalized gradients and space decomposition techniques suited for the norm and other nonsmooth performance criteria. For the class of max-functions, which possesses the so-called primal-dual gradient structure, we compute smooth trajectories along which certain second-order expansions can be obtained. We also give the first- and second-order derivatives of primal-dual function in the space of decision variables under some assumptions.
"The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations." Abstr. Appl. Anal. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/845017