Abstract
The paper deals with the problem of finding the global minimum of a function in a subset of \(\mathbb {R}^{n}\) described by values of solutions to a system of semilinear parabolic equations. We propose a construction of a new dual dynamic programming to formulate a new optimization problem. As a consequence we state and prove a verification theorem for the global minimum and investigate a dual optimal feedback control for the global optimization.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)
Galewska, E., Nowakowski, A.: A dual dynamic programming for multidimensional elliptic optimal control problems. Numer. Funct. Anal. Optim. 27, 279–289 (2006)
Nowakowski, A.: The dual dynamic programming. Proc. Am. Math. Soc. 116, 1089–1096 (1992)
Nowakowski, A., Sokolowski, J.: On dual dynamic programming in shape control. Commun. Pure Appl. Anal. 11, 2473–2485 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Kaźmierczak, A., Nowakowski, A. (2020). New Dynamic Programming Approach to Global Optimization. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)