PARTIALLY-FINITE PROGRAMMING IN L-1 AND THE EXISTENCE OF MAXIMUM ENTROPY ESTIMATES

被引：63

作者：

Borwein, J. M. ^{[1
]}

Lewis, A. S. ^{[1
]}

机构：

[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

来源：

SIAM JOURNAL ON OPTIMIZATION | 1993年 / 3卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

convex analysis; duality; existence; generalized solution; image reconstruction; maximum entropy method; moment problem; partially finite program; spectral estimation;

D O I：

10.1137/0803012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Best entropy estimation is a technique that has been widely applied in many areas of science. It consists of estimating an unknown density from some of its moments by maximizing some measure of the entropy of the estimate. This problem can be modelled as a partially-finite convex program, with an integrable function as the variable. A complete duality and existence theory is developed for this problem and for an associated extended problem which allows singular, measure-theoretic solutions. This theory explains the appearance of singular components observed in the literature when the Burg entropy is used. It also provides a unified treatment of existence conditions when the Burg, Boltzmann-Shannon, or some other entropy is used as the objective. Some examples are discussed.

引用

页码：248 / 267

页数：20