Entropy minimization, DAD problems, and doubly stochastic kernels

J. M. Borwein; A. S. Lewis; R. D. Nussbaum

doi:10.1006/jfan.1994.1089

Entropy minimization, DAD problems, and doubly stochastic kernels

J. M. Borwein, A. S. Lewis, R. D. Nussbaum

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

The classical DAD problem asks, for a square matrix A with nonnegative entries, when it is possible to find positive diagonal matrices D₁ and D₂ with D₁AD₂ doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.

Original language	English (US)
Pages (from-to)	264-307
Number of pages	44
Journal	Journal of Functional Analysis
Volume	123
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1994.1089
State	Published - Aug 1 1994

All Science Journal Classification (ASJC) codes

Analysis

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title = "Entropy minimization, DAD problems, and doubly stochastic kernels",

abstract = "The classical DAD problem asks, for a square matrix A with nonnegative entries, when it is possible to find positive diagonal matrices D1 and D2 with D1AD2 doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.",

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N2 - The classical DAD problem asks, for a square matrix A with nonnegative entries, when it is possible to find positive diagonal matrices D1 and D2 with D1AD2 doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.

AB - The classical DAD problem asks, for a square matrix A with nonnegative entries, when it is possible to find positive diagonal matrices D1 and D2 with D1AD2 doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.

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Entropy minimization, DAD problems, and doubly stochastic kernels

Abstract

All Science Journal Classification (ASJC) codes

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