Sufficient conditions for the convergence of nonautonomous stochastic search for a global minimum
cytuj
pobierz pliki
RIS BIB ENDNOTEWybierz format
RIS BIB ENDNOTESufficient conditions for the convergence of nonautonomous stochastic search for a global minimum
Data publikacji: 05.06.2012
Universitatis Iagellonicae Acta Mathematica, 2011, Tom 49, s. 73 - 83
https://doi.org/10.4467/20843828AM.12.005.0457Autorzy
Sufficient conditions for the convergence of nonautonomous stochastic search for a global minimum
The majority of stochastic optimization algorithms can be written in the general form xt+1 = Tt(xt; yt), where xt is a sequence of points and parameters which are transformed by the algorithm, Tt are the methods of the algorithm and yt represent the randomness of the algorithm. We extend the results of papers [11] and [14] to provide some new general conditions under which the algorithm finds a global minimum with probability one.
1. Appel M. J., Labarre R., Radulovic D., On Accelerated Random Search, SIAM J. Optim., 14 (2003), 708-731.
2. Beyer H. G., Schwefel H. P., Evolution Strategies - A Comprehensive Introduction, Natural Computing, 1 (2002), 3-52.
3. Billingsley P., Convergence of Probability Measures, Second Edition, A Wiley-Interscience Publication, 1999.
4. Clerc M., Kennedy J., The Particle Swarm - Explosion, Stability, and Convergence in a Multidimensional Complex Space, IEEE Transactions on Evolutionary Computation, 6 (2002).
5. Clerc M., Particle Swarm Optimization, ISTE Ltd, London, 2006.
6. Dudley R. M., Real Analysis and Probability, Cambridge University Press, 2004.
7. Lasota A., Mackey M., Chaos, Fractals and Noise, Springer Verlag, 1994.
8. Meyn S., Twedie R., Markov Chains and Stochastic Stability, Springer Verlag, London, 1993.
9. Ombach J., Stability of evolutionary algorithms, J. Math. Anal. Appl., 342 (2008), 326-333.
10. Ombach J., A Proof of Convergence of General Stochastic Search for Global Minimum, Journal of Di erence Equations and Applications, 13 (2007), 795-802.
11. Ombach J., Tar lowski D., Nonautonomous Stochastic Search in Global Optimization, Preprint.
12. Radwanski M., Convergence of nonautonomous evolutionary algorithm, Univ. Iagel. Acta Math., 45 (2007), 197-206.
13. Rudolph G., Convergence of Evolutionary Algorithms in General Search Spaces, 50-54, Proceedings of the Third IEEE Conference on Evolutionary Computation, Piscataway, IEEE Press, NJ, 1996.
14. Tarlowski D., Non-autonomous Stochastic Search for Global Minimum in Continuous Optimization, Preprint.
15. Tarlowski D., Global Convergence of Stochastic Optimization Algorithms, Preprint.
16. Zhigljavsky A., Zilinskas A., Stochastic Global Optimization, Springer, New York, 2008.
Informacje: Universitatis Iagellonicae Acta Mathematica, 2011, Tom 49, s. 73 - 83
Typ artykułu: Oryginalny artykuł naukowy
Tytuły:
Sufficient conditions for the convergence of nonautonomous stochastic search for a global minimum
Sufficient conditions for the convergence of nonautonomous stochastic search for a global minimum
Instytut Matematyki, Uniwersytet Jagielloński, Kraków, Polska
Publikacja: 05.06.2012
Status artykułu: Otwarte
Licencja: Żadna
Udział procentowy autorów:
Korekty artykułu:
-Języki publikacji:
AngielskiLiczba wyświetleń: 1765
Liczba pobrań: 993