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• W2611807022 startingPage "259" @default.
• W2611807022 abstract "The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix functions, many of which are of importance in quantum information theory. In this paper we show how to approximate the matrix logarithm with functions that preserve operator concavity and can be described using the feasible regions of semidefinite optimization problems of fairly small size. Such approximations allow us to use off-the-shelf semidefinite optimization solvers for convex optimization problems involving the matrix logarithm and related functions, such as the quantum relative entropy. The basic ingredients of our approach apply, beyond the matrix logarithm, to functions that are operator concave and operator monotone. As such, we introduce strategies for constructing semidefinite approximations that we expect will be useful, more generally, for studying the approximation power of functions with small semidefinite representations." @default.
• W2611807022 created "2017-05-12" @default.
• W2611807022 creator A5017261970 @default.
• W2611807022 creator A5031935416 @default.
• W2611807022 creator A5037774037 @default.
• W2611807022 date "2018-03-21" @default.
• W2611807022 modified "2023-10-16" @default.
• W2611807022 title "Semidefinite Approximations of the Matrix Logarithm" @default.
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• W2611807022 doi "https://doi.org/10.1007/s10208-018-9385-0" @default.
• W2611807022 hasPublicationYear "2018" @default.
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