1. The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations.
- Author
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Ming Huang, Li-Ping Pang, Xi-Jun Liang, and Zun-Quan Xia
- Subjects
- *
EIGENVALUES , *SYMMETRIC matrices , *MAXIMA & minima , *MATHEMATICAL functions , *MATHEMATICAL optimization , *MATHEMATICAL expansion - 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 UV 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 Rm under some assumptions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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