Optimality Conditions and Algorithms for Direct Optimizing the Partial Differential Equations

DOI: 10.4236/eng.2012.47051   PDF   HTML     4,343 Downloads   6,294 Views   Citations

Abstract

New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE). Appropriate algo-rithms for unconstrained minimizing a functional are considered and tested. To construct the algorithms, new form of NCO is used. Such approach demonstrates fast uniform convergence at optimal solution in infinite-dimensional space.

Share and Cite:

V. Tolstykh, "Optimality Conditions and Algorithms for Direct Optimizing the Partial Differential Equations," Engineering, Vol. 4 No. 7, 2012, pp. 390-393. doi: 10.4236/eng.2012.47051.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] N. M. Alexandrov, “Optimization of Engineering Systems Governed by Differential Equations,” SIAG/OPT Views & News, Vol. 11, No. 2, 2000, pp. 1-4.
[2] R. M. Lewis, “The Adjoint Approach in a Nutshell,” SIAG/OPT Views & News, Vol. 11, No. 2, 2000, pp. 9-12.
[3] V. K. Tolstykh, “Direct Extreme Approach for Optimization of Distributed Parameter Systems,” Yugo-Vostok, Donetsk, 1997.
[4] V. K. Tolstykh, “New First-Order Algorithms for Optimal Control under Large and Infinite-Dimensional Objective Functions New First-Order Algorithm for Optimal Control with High Dimensional Quadratic Objective,” Proceedings of the 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Lausanne, 21-25 August 2000. http://metronu.ulb.ac.be/imacs/lausanne/CP/215-3.pdf
[5] R. H. W. Hoppe and S. I. Petrova, “Applications of the Newton Interior-Point Method for Maxwell’s Equations,” Proceedings of the 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Lausanne, 21-25 August 2000. http://metronu.ulb.ac.be/imacs/lausanne/SP/107-7.pdf
[6] C. T. Kelly, “Iterative Methods for Optimization,” SIAM, Philadelphia, 1999. doi:10.1137/1.9781611970920
[7] J. Nocedal, S. J. Wright, “Numerical Optimization,” Springer, New York, 1999. doi:10.1007/b98874

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.