The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations. (17th February 2014)

• Record Type: Journal Article
• Authors: Huang, Ming; Pang, Li-Ping; Liang, Xi-Jun; Xia, Zun-Quan
• Other Names: Cao Jinde Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-17
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/845017
• Languages: English
• ISSNs: 1085-3375

Abstract

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 and𝒰 𝒱 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 variablesR m under some assumptions.