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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 60, 2011 - Issue 4
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Original Articles

Spectral self-concordant functions in the space of two-by-two symmetric matrices

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Pages 441-449 | Received 13 Feb 2009, Accepted 16 Sep 2009, Published online: 26 Apr 2010
 

Abstract

We show that given a two-variable, symmetric, ϑ-self-concordant function f, the spectral function F = f ○ λ is 2(1 + 3ϑ)-self-concordant. Correspondingly, if f is ϑ-self-concordant barrier, then 4(1 + 3ϑ)2 F is a 4(1 + 3ϑ)2ϑ-self-concordant barrier.

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Acknowledgements

J. Peña is supported by NSF grant CCF-0830533. H. Sendov is supported by NSERC.

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