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

Title: On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems
Creator: Borwein, Jonathon M.
Relation: Mathematical Programming Vol. 61, Issue 1-3, p. 251-261
Publisher Link: http://dx.doi.org/10.1007/BF01582150
Publisher: Springer
Resource Type: journal article
Date: 1993
Description: We analyse several examples where the maximum entropy solution to a system of equations exists but fails to satisfy the natural (dual) formula. These examples highlight the role that finiteness of the number of constraints has in the efficacy of maximum entropy type estimation and reconstruction. We also provide two regularization processes which repair the problem.
Subject: Boltzmann—Shannon entropy; maximum entropy estimates; Fenchel duality; Fredholm equations; Lagrange multipliers; dual convex programs; duality gaps; regularization; penalization
Identifier: http://hdl.handle.net/1959.13/940983
Identifier: uon:13146
Identifier: ISSN:0025-5610
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format