Neural networks for solving least absolute and related problems

Neurocomputing

Volumn 19, Issue 1-3, 1998, Pages 13-21

  Xia, Youshen ^a   Wang, Jun ^b  

^a NANJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

L1 norm minimization; Neural networks

Indexed keywords

MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING; VECTORS;

LEAST ABSOLUTE DEVIATIONS PROBLEMS; LINEAR EQUATIONS;

NEURAL NETWORKS;

ARTICLE; LINEAR ENERGY TRANSFER; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEASUREMENT; NERVE CELL NETWORK; PRIORITY JOURNAL; SOLVATION;

EID: 0345267235     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(97)00082-9     Document Type: Article

References (14)

1. Huber P.J. Robust Statistics. 1981;Wiley, New York.
2. Osborne M.R. Finite algorithms in optimization and Data Analysis. 1985;Wiley, New York.
3. Bloomfield P., Steiger W.L. Least Absolute Deviations Theory Applications Algorithms. 1983;Birkha-user, Boston.
4. A. Dax, The L solution of linear equations subject to linear constraints, SIAM Sci. Comput. 10(10) 328.
5. Hopfield J.J., Tank D.W. Neural computation of decisions in optimization problems. Biol. Cybernet. 52:1986;141.
6. Tank D.W., Hopfield J.J. Simple neural optimization networks: an A/D converter, signal decision circuit and a linear programming circuit. IEEE Trans. Circuits Systems. 33(5):1986;553.
7. Rodriguez-Vazquez A., Dominguez-Castro R., Rueda A., Huerlas J.L., Sanchez-Sinenclo E. Nonlinear switched capacitor neural network for optimization problems. IEEE Trans. Circuit Systems. 37(3):1990;384.
8. Wang J. Analysis and design of a recurrent neural network for linear programming. IEEE Trans. Circuit Systems. 7(4):1994;629.
9. Xia Y. A new neural network for solving linear programming and its application. IEEE Trans. Neural Networks. 7(2):1996;525.
10. Xia Y., Wang J. Neural network for solving linear programming with bounded variable. IEEE Trans. Neural Networks. 2:1995;515.
11. Cichocki A., Unbobauen R. Neural Networks for optimization and Signal Processing. 1993;Wiley, West Sussex.
12. S.H. Zak, Stefen Hui, Solving linear programming problems with neural networks: A comparative study, IEEE Trans. Neural Networks 6(1) (1995).
13. Kinderleher D., Stampcchia G. An Introduction to variational inequalities and their applicaton. 1980;Academic Press, Italiana.
14. He B.S. Solution and applications of a class of general linear variational inequalities. Chinese Science. 2:1995;939-945.