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

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

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.

Suggested Citation

  • Ming Huang & Li-Ping Pang & Xi-Jun Liang & Zun-Quan Xia, 2014. "The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, February.
    • Handle: RePEc:hin:jnlaaa:845017
    DOI: 10.1155/2014/845017
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