# Optimizing condition numbers

Maréchal, Pierre and Ye, Jane Optimizing condition numbers. (2009) SIAM Journal on Optimization (SIOPT), 20 (2). 935-947. ISSN 1052-6234

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Official URL: http://dx.doi.org/10.1137/080740544

## Abstract

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers.

Item Type: Article International peer-reviewed journal Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)Other partners > Victoria University (CANADA) download Pierre Maréchal 14 May 2013 15:08

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