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2014 The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations
Ming Huang, Li-Ping Pang, Xi-Jun Liang, Zun-Quan Xia
Abstr. Appl. Anal. 2014: 1-12 (2014). DOI: 10.1155/2014/845017

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.

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

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023185
MathSciNet: MR3176773
Digital Object Identifier: 10.1155/2014/845017

Rights: Copyright © 2014 Hindawi

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