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New Dynamic Programming Approach to Global Optimization

  • Anna KaźmierczakEmail author
  • Andrzej Nowakowski
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

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.

Keywords

Global optimization Dynamic programming Feedback control 

References

  1. 1.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)Google Scholar
  2. 2.
    Galewska, E., Nowakowski, A.: A dual dynamic programming for multidimensional elliptic optimal control problems. Numer. Funct. Anal. Optim. 27, 279–289 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Nowakowski, A.: The dual dynamic programming. Proc. Am. Math. Soc. 116, 1089–1096 (1992)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Nowakowski, A., Sokolowski, J.: On dual dynamic programming in shape control. Commun. Pure Appl. Anal. 11, 2473–2485 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of LodzLodzPoland

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