The space decomposition theory for a class of eigenvalue optimizations

The space decomposition theory for a class of eigenvalue optimizations

0.00 Avg rating0 Votes
Article ID: iaor2014697
Volume: 58
Issue: 2
Start Page Number: 423
End Page Number: 454
Publication Date: Jun 2014
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: matrices
Abstract:

In this paper we study optimization problems involving eigenvalues of symmetric matrices. One of the difficulties with numerical analysis of such problems is that the eigenvalues, considered as functions of a symmetric matrix, are not differentiable at those points where they coalesce. Here we apply the 𝒰 equ1 ‐Lagrangian theory to a class of D.C. functions (the difference of two convex functions): the arbitrary eigenvalue function λ i , with affine matrix‐valued mappings, where λ i is a D.C. function. We give the first‐and second‐order derivatives of 𝒰 equ2 ‐Lagrangian in the space of decision variables R m when transversality condition holds. Moreover, an algorithm framework with quadratic convergence is presented. Finally, we present an application: low rank matrix optimization; meanwhile, list its 𝒱𝒰 equ3 decomposition results.

Reviews

Required fields are marked *. Your email address will not be published.