Abstract
The goal of this work is to show that a positive automata iteration is the natural hill-climbing strategy of a subnorm or norm optimization problem.
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References
Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.M. Teller, E.J. Teller, J. Chem. Phys. 21, 1087 (1953).
Garey, M.R., D.S. Johnson, Computers and intractability. Freeman, N. York (1979).
Kirkpatrick, S., C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. Science 220(4598), 671–680 (1983).
Van Laarhoven, P.J.M., E.H.L. Aarts, Simulated annealing: theory and applications. D. Reidel Publ., Kluwer (1987).
Mezard, M., G. Parisi, M. Virasoro, Spin glass theory and beyond. World Scientific (1987).
Goles, E., S. Martinez, Neural and automata networks. Kluwer (1990).
Hopfield, J.J., Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79, USA, 2554–2558 (1982).
Hopfield, J.J., D.W. Tank, Neural computation of decisions in optimization problems. Biol. Cybernetic 52, 141–152 (1985).
Householder, A.S., The theory of matrices in numerical analysis. Blaisdell Publ., New York, 1964.
Laurent, J.P., Approximation et optimisation, Herrmann, Paris, 1972.
Schwartz, L., Analyse: topologie générale et analyse fonctionnelle, Herrmann, Paris, 1970.
Robert, F., Calcul du rapport maximal de deux normes sur IR n, RIRO (5), 97–118, 1967.
Gastinel, N., Analyse numérique linéaire, Herrmann, Paris, 1966.
Rockafellar, R.T., Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970.
Giles, J.R., Convex analysis with application in differentiation of convex functions. Pitman Adv. Publ. Prog., Boston, 1982.
Janssen, A.J.E.M., An optimization problem related to neural networks, Information Processing Letters 37, 155–157, 1991.
Barahona, F., Application de l’optimisation combinatoire á certains modèles de verres de spin, Doctoral Thesis, IMAG, Grenoble, France, 1980.
Peterson, C., J. Anderson, Neural networks and NP-complete optimization problems; A performance study on the graph bisection problem, Complex Systems, 2, 59–89, 1988.
Cominetti, R., Automata networks and optomization of differences of convex functions, Preprint, 1990.
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© 1992 Springer Science+Business Media Dordrecht
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Goles, E., Martinez, S. (1992). Automata Networks Strategies for Optimization Problems. In: Goles, E., Martínez, S. (eds) Statistical Physics, Automata Networks and Dynamical Systems. Mathematics and Its Applications, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2578-9_3
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DOI: https://doi.org/10.1007/978-94-011-2578-9_3
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