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:
-
- 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}
}
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