A New Class of Self-Concordant Barriers from Separable Spectral Functions

  • Javier F. Peña
  • Hristo Sendov
    • Categories Convex Optimization Tags , , , Short URL: https://optimization-online.org/?p=10232

    Given a separable strongly self-concordant function f:Rn -> R, we show the associated spectral function F(X)= (foL)(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 O^2F(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 -log(x1)-...-log(xn) and -log det(X) and gives a partial solution to a conjecture of L. Tuncel.

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    Submitted for publication in Mathematical Programming

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