On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems

DOI10.1007/BF01582150zbMath0796.94002OpenAlexW2007048854WikidataQ56935943 ScholiaQ56935943MaRDI QIDQ1315418

Jonathan M. Borwein

Publication date: 27 March 1994

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01582150

zbMATH Keywords

Lagrange multipliersregularizationpenalizationFenchel dualityBoltzmann-Shannon entropyFredholm equationsmaximum entropy solutionduality gapsdual convex programsmaximum entropy estimates

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Existence theories for problems in abstract spaces (49J27) Measures of information, entropy (94A17) Fredholm integral equations (45B05)

Related Items (4)

Solving Fredholm equations by maximum entropy on the mean. Application to superresolution ⋮ Minimization of entropy functionals ⋮ Inference in ϕ-families of distributions ⋮ Duality and Convex Programming

Cites Work

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• Convergence of Best Entropy Estimates
• Convergence of best phi -entropy estimates
• Maximum Entropy Regularization for Fredholm Integral Equations of the First Kind
• Strong Rotundity and Optimization
• Convex Analysis

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