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Spectral self-concordant functions in the space of two-by-two symmetric matrices |
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| Abstract: | We show that given a two-variable, symmetric, ?-self-concordant function f, the spectral function F = f ○ λ is 2(1 + 3?)-self-concordant. Correspondingly, if f is ?-self-concordant barrier, then 4(1 + 3?)2 F is a 4(1 + 3?)2?-self-concordant barrier. |
| Keywords: | self-concordant barrier self-concordant function spectral function eigenvalue symmetric matrix |