An efficient computational procedure for solving entropy optimization problems with infinitely many linear constraints
type: Item
instance of: scholarly article
title: An efficient computational procedure for solving entropy optimization problems with infinitely many linear constraints
zbMATH Open document ID: 0872.65054
DOI: 10.1016/0377-0427(95)00266-9
author: Shu-Cherng Fang
author: H.-S. Jacob Tsao
published in: Journal of Computational and Applied Mathematics
publication date: 1997-10-08T00:00:00Z
review text: One considers the entropy optimization problem with an infinite number of linear constraints \[ \inf \sum^n_{j=1} x_j\ln x_j \text \;{ s.t. } \sum^n_{j=1} g_j(t)x_j\geq h(t),\;t\in T, \] where \(T\) is a compact metric space and \(g_1,\dots,g_n\) and \(h\) are real-valued continuous functions on \(T\). A cutting-plane type algorithm for solving the entropy optimization with an infinite number of linear constraints is proposed. In each iteration one solves a finite entropy optimization problem and adds one more constraint if an optimal solution is not identified. Under a mild condition the algorithm converges. Preliminary computational experience confirms the efficiency of the proposed method.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 933157
zbMATH Keywords: infinite constraint set
zbMATH Keywords: duality
zbMATH Keywords: convergence
zbMATH Keywords: semi-infinite programming
zbMATH Keywords: numerical examples
zbMATH Keywords: entropy optimization problem
zbMATH Keywords: compact metric space
zbMATH Keywords: cutting-plane type algorithm
reviewed by: Dorel I. Duca
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00266-9
OpenAlex ID: W2039099506
cites work: Q3042910
cites work: Q3879064
cites work: Curved search methods for unconstrained optimization
cites work: The role of duality in optimization problems involving entropy functionals with applications to information theory
cites work: Duality Relationships for Entropy-Like Minimization Problems
cites work: Partially-Finite Programming in $L_1 $ and the Existence of Maximum Entropy Estimates
cites work: On some methods for entropy maximization and matrix scaling
cites work: Minimum cross-entropy analysis with entropy-type constraints
cites work: Quadratically constrained minimum cross-entropy analysis
cites work: Linear programming with entropic perturbation
cites work: Linear programming with inequality constraints via entropic perturbation
cites work: A quadratically convergent global algorithm for the linearly-constrained minimum cross-entropy problem
cites work: An inexact approach to solving linear semi-infinite programming problems
cites work: Semi-infinite programming and applications. An International Symposium, Austin, Texas, September 8-10, 1981
cites work: Q4158954
cites work: An approach to nonlinear programming
cites work: Q3738922
cites work: Geometric Programming
cites work: Q5638112
cites work: Minimum cross-entropy spectral analysis
cites work: On the optimal entropy analysis
description: scientific article; zbMATH DE number 933157