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Leonid Faybusovich(lfaybusogmail.com) Abstract: Let $g$ be a continuously differentiable function whose derivative is matrix monotone on positive semiaxis. Such a function induces a function $\phi (x)=tr(g(x))$ on the cone of squares of an arbitrary Euclidean Jordan algebra. We show that $\phi (x) \ln \det(x)$ is a selfconcordant function on the interior of the cone. We also show that $\ln (t\phi (x))\ln \det (x)$ is $\sqrt{\frac{5}{3}}(r+1)$selfconcordant barrier on the epigraph of $\phi ,$ where $r$ is the rank of the Jordan algebra. The case $\phi (x)=tr(x\ln x)$ is discussed in detail. Keywords: quantum entropy,matrix monotonicity,selfconcordance Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Linear, Cone and Semidefinite Programming Citation: Preprint,GRIPS,August 2014 Download: [PDF] Entry Submitted: 08/28/2014 Modify/Update this entry  
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