Partially-Finite Programming in $L_1 $ and the Existence of Maximum Entropy Estimates
- 1 May 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 3 (2) , 248-267
- https://doi.org/10.1137/0803012
Abstract
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.Keywords
This publication has 32 references indexed in Scilit:
- Moment-Matching and Best Entropy EstimationJournal of Mathematical Analysis and Applications, 1994
- Partially finite convex programming, Part II: Explicit lattice modelsMathematical Programming, 1992
- Dual Methods in Entropy Maximization. Application to Some Problems in CrystallographySIAM Journal on Optimization, 1992
- Convergence of Best Entropy EstimatesSIAM Journal on Optimization, 1991
- Duality Relationships for Entropy-Like Minimization ProblemsSIAM Journal on Control and Optimization, 1991
- On the convergence of moment problemsTransactions of the American Mathematical Society, 1991
- A Dual Approach to Multidimensional $L_p$ Spectral Estimation ProblemsSIAM Journal on Control and Optimization, 1988
- Maximum-Entropy and Bayesian Methods in Science and EngineeringPublished by Springer Nature ,1988
- A simple constraint qualification in infinite dimensional programmingMathematical Programming, 1986
- Notes on maximum-entropy processing (Corresp.)IEEE Transactions on Information Theory, 1973