Smooth convex approximation to the maximum eigenvalue function


Chen, Xin, Qi, Houduo, Qi, Liqun and Teo, Kok-Lay (2004) Smooth convex approximation to the maximum eigenvalue function. Journal of Global Optimization, 30, (2-3), 253-270. (doi:10.1007/s10898-004-8271-2).

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Description/Abstract

In this paper, we consider smooth convex approximations to the maximum eigenvalue function. To make it applicable to a wide class of applications, the study is conducted on the composite function of the maximum eigenvalue function and a linear operator mapping m to , the space of n-by-n symmetric matrices. The composite function in turn is the natural objective function of minimizing the maximum eigenvalue function over an affine space in . This leads to a sequence of smooth convex minimization problems governed by a smoothing parameter. As the parameter goes to zero, the original problem is recovered. We then develop a computable Hessian formula of the smooth convex functions, matrix representation of the Hessian, and study the regularity conditions which guarantee the nonsingularity of the Hessian matrices. The study on the well-posedness of the smooth convex function leads to a regularization method which is globally convergent.

Item Type: Article
Related URLs:
Keywords: matrix representation, spectral function, symmetric function, tikhonov regularization
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29650
Date Deposited: 11 May 2006
Last Modified: 27 Mar 2014 18:18
Contact Email Address: hdqi@soton.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/29650

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