Chapter

Nonlinear Analysis and Variational Problems

Volume 35 of the series Springer Optimization and Its Applications pp 465-490

Date:

Generating Eigenvalue Bounds Using Optimization

  • Henry WolkowiczAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo

* Final gross prices may vary according to local VAT.

Get Access

Abstract

This paper illustrates how optimization can be used to derive known and new theoretical results about perturbations of matrices and sensitivity of eigenvalues. More specifically, the Karush–Kuhn–Tucker conditions, the shadow prices, and the parametric solution of a fractional program are used to derive explicit formulae for bounds for functions of matrix eigenvalues.