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Title: Neural network models for Linear Programming

Abstract

The purpose of this paper is to present a neural network that solves the general Linear Programming (LP) problem. In the first part, we recall Hopfield and Tank's circuit for LP and show that although it converges to stable states, it does not, in general, yield admissible solutions. This is due to the penalization treatment of the constraints. In the second part, we propose an approach based on Lagragrange multipliers that converges to primal and dual admissible solutions. We also show that the duality gap (measuring the optimality) can be rendered, in principle, as small as needed. 11 refs.

Authors:
; ; ;  [1]
  1. Oak Ridge National Lab., TN (USA)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
DOE/ER
OSTI Identifier:
5347615
Report Number(s):
CONF-900116-2
ON: DE89015974; CNN: DARPA1868-A037-A1
DOE Contract Number:  
AC05-84OR21400
Resource Type:
Conference
Resource Relation:
Conference: International joint conference on neural networks, Washington, DC (USA), 15-19 Jan 1990
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMPUTER NETWORKS; LINEAR PROGRAMMING; ALGORITHMS; MATHEMATICAL MODELS; OPTIMIZATION; MATHEMATICAL LOGIC; PROGRAMMING; 990200* - Mathematics & Computers

Citation Formats

Culioli, J C, Protopopescu, V, Britton, C, and Ericson, N. Neural network models for Linear Programming. United States: N. p., 1989. Web.
Culioli, J C, Protopopescu, V, Britton, C, & Ericson, N. Neural network models for Linear Programming. United States.
Culioli, J C, Protopopescu, V, Britton, C, and Ericson, N. 1989. "Neural network models for Linear Programming". United States. https://www.osti.gov/servlets/purl/5347615.
@article{osti_5347615,
title = {Neural network models for Linear Programming},
author = {Culioli, J C and Protopopescu, V and Britton, C and Ericson, N},
abstractNote = {The purpose of this paper is to present a neural network that solves the general Linear Programming (LP) problem. In the first part, we recall Hopfield and Tank's circuit for LP and show that although it converges to stable states, it does not, in general, yield admissible solutions. This is due to the penalization treatment of the constraints. In the second part, we propose an approach based on Lagragrange multipliers that converges to primal and dual admissible solutions. We also show that the duality gap (measuring the optimality) can be rendered, in principle, as small as needed. 11 refs.},
doi = {},
url = {https://www.osti.gov/biblio/5347615}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 1989},
month = {Sun Jan 01 00:00:00 EST 1989}
}

Conference:
Other availability
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