A New Class of Self-Concordant Barriers from Separable Spectral Functions
نویسندگان
چکیده
Given a separable strongly self-concordant function f : Rn → R, we show the associated spectral function F(X) = ( f ◦ λ )(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f (x) is separable self-concordant barrier then O2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O ≤ 22. This generalizes the relationship between the standard logarithmic barriers −∑i=1 logxi and − logdetX and gives a partial solution to a conjecture of L. Tunçel.
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