Abstract
Canonical duality theory for solving the well-known benchmark test problem of stochastic Rosenbrock function is explored by two canonical transformations. Global optimality criterion is analytically obtained, which shows that the stochastic disturbance of these parameters could be eliminated by a proper canonical dual transformation. Numerical simulations illustrate the canonical duality theory is potentially powerful for solving this benchmark test problem and many other challenging problems in global optimization and complex network systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Rosenbrock, H.H.: An automatic method for finding the greatest or least value of a function. The Computer Journal 3, 175–184 (1960)
Yang, X.S., Deb, S.: Engineering optimization by cuckoo search. Int. J. Math. Modelling Num. Optimisation 1, 330–343 (2010)
Gao, D.Y.: Duality, triality and complementary extremum principles in nonconvex parametric variational problems with applications. IMA J. Appl. Math. 61, 199–235 (1998)
Gao, D.Y.: Pure complementary energy principle and triality theory in finite elasticity. Mech. Res. Commun. 26(1), 31–37 (1999)
Gao, D.Y.: General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Meccanica 34, 169–198 (1999)
Gao, D.Y.: Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Kluwer Academic, Dordrecht (2000)
Gao, D.Y.: Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J. Glob. Optim. 17, 127–160 (2000)
Gao, D.Y.: Perfect duality theory and complete solutions to a class of global optimization problems. Optim. 52, 467–493 (2003)
Gao, D.Y.: Perfect duality theory and complete solutions to a class of global optimization problems. Optimization 52, 467–493 (2003)
Gao, D.Y.: Nonconvex semi-linear problems and canonical dual solutions. In: Gao, D.Y., Ogden, R.W. (eds.) Advances in Mechanics and Mathematics, vol. II, pp. 261–312. Kluwer Academic, Dordrecht (2003)
Gao, D.Y.: Canonical duality theory and solutions to constrained nonconvex quadratic programming. J. Glob. Optim. 29, 377–399 (2004)
Gao, D.Y.: Solutions and optimality to box constrained nonconvex minimization problems. J. Ind. Manag. Optim. 3(2), 293–304 (2007)
Gao, D.Y.: Canonical duality theory: theory, method, and applications in global optimization. Comput. Chem. 33, 1964–1972 (2009)
Gao, D.Y., Wu, C.Z.: On the triality theory in global optimization. J. Global Optimization (2010)
Gao, D.Y., Zhang, J.P.: Canonical Duality Theory for Solving Minimization Problem of Rosenbrock Function. arxiv.org/abs/1108.1241v1
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, C., Gao, D.Y. (2012). Global Minimizer of Large Scale Stochastic Rosenbrock Function: Canonical Duality Approach. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34478-7_82
Download citation
DOI: https://doi.org/10.1007/978-3-642-34478-7_82
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34477-0
Online ISBN: 978-3-642-34478-7
eBook Packages: Computer ScienceComputer Science (R0)