Linear programming with inequality constraints via entropic perturbation
type: Item
instance of: scholarly article
title: Linear programming with inequality constraints via entropic perturbation
zbMATH Open document ID: 0843.90080
DOI: 10.1155/S0161171296000257
author: H.-S. Jacob Tsao
author: Shu-Cherng Fang
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/47472
review text: Summary: A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. An \(\varepsilon\)-optimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Since cross-entropy minimization subject to linear inequality constraints is a special case of the perturbed linear program, the duality result becomes readily applicable. Many standard constrained optimization techniques can be specialized to solve the dual program. Such specializations, made possible by the simplicity of the constraints, significantly reduce the computational effort usually incurred by these methods. Immediate applications of the theory developed include an entropic path-following approach to solving linear semi-infinite programs with an infinite number of inequality constraints and the widely used entropy optimization models with linear inequality and/or equality constraints.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C34
zbMATH DE Number: 844418
zbMATH Keywords: perturbation method
zbMATH Keywords: dual convex programming
zbMATH Keywords: entropic perturbation
zbMATH Keywords: \(\varepsilon\)-optimal solution
zbMATH Keywords: cross-entropy minimization
zbMATH Keywords: linear inequality constraints
zbMATH Keywords: entropic path-following
MaRDI profile type: Publication
OpenAlex ID: W2122028571
description: scientific article; zbMATH DE number 844418