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

Ming Huang, Li-Ping Pang, Xi-Jun Liang and Zun-Quan Xia

Abstract and Applied Analysis, 2014, vol. 2014, 1-12

Abstract:

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:845017

DOI: 10.1155/2014/845017

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