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Javier Pena(jfpandrew.cmu.edu) Abstract: Given a separable strongly selfconcordant function f:Rn > R, we show the associated spectral function F(X)= (foL)(X) is also strongly selfconcordant function. In addition, there is a universal constant O such that, if f(x) is separable selfconcordant barrier then O^2F(X) is a selfconcordant 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. Keywords: Selfconcordant barrier, strongly selfconcordant, selfconcordant function, spectral function, Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Submitted for publication in Mathematical Programming Download: [PDF] Entry Submitted: 09/07/2007 Modify/Update this entry  
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