Abstract
Algorithms for minimizing a function based on continuous descent methods following the gradient relative to some riemannian metric suffer from the twin problems of converging to local, rather than global, minima and giving little indication about an approximate answer until the process has nearly converged. Simulated annealing addresses these problems through the introduction of stochastic terms, however the rate of convergence associated with the method can be unacceptably slow. In this paper we discuss a modification of simulated annealing which approaches a minimum through a damped oscillatory path. The characteristics of the path, including its tendency to be irregular, reflect the properties of the function being minimized. The oscillatory algorithm involves both a temperature and coupling parameters, giving it considerable flexibility.
This work was supported in part by the National Science Foundation under Engineering Research Center Program, NSF EEC-94-02384, by the US Army Research Office under grant DAAL03-92-G-0115(Center for Intelligent Control Systems), and by the Office of Naval Research under Grant N00014-1887
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References
S. Geeman and C. R. Hwang, “Diffusions for Global Optimization,” SIAM J. on Control and Optimization, Vol. 24, pp. 1031–1043, 1986.
Richard Holley, Shigeo Kusuoka, and Daniel Strook, “Asymptotics of the Spectral Gap with Applications to the Theory of Simulated Annealing,” Journal of Functional Analysis, vol. 83, pp. 333–347, 1989.
Saul B. Gelfand and S. K. Mitter, “Metropolis-Type Annealing Algorithms for Global Optimization in ℝd,” SIAM J. on Control and Optimization, Vol. 31, pp. 111–131, 1993.
R. W. Brockett and Jan Willems, “Stochastic Control and the Second law of Thermodynamics,” IEEE conference on Decision and Control, IEEE, New York, 1979.
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Brockett, R. (1997). Oscillatory Descent for Function Minimization. In: Alber, M., Hu, B., Rosenthal, J. (eds) Current and Future Directions in Applied Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2012-1_12
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DOI: https://doi.org/10.1007/978-1-4612-2012-1_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7380-6
Online ISBN: 978-1-4612-2012-1
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