Optimality Conditions and Algorithms for Direct Optimizing the Partial Differential Equations ()
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
|