Implicit Filtering and Optimal Design Problems

  • P. Gilmore
  • C. T. Kelley
  • C. T. Miller
  • G. A. Williams
Part of the Progress in Systems and Control Theory book series (PSCT, volume 19)

Abstract

Implicit filtering is a form of the gradient projection method of Bertsekas in which the stepsize in a difference approximation of the gradient is changed as the iteration progresses. In this way the algorithm is able to avoid certain types of local minima and in some cases find accurate approximations to the global minimum. The algorithm is particularly effective in avoiding local minima that are caused by high-frequency low-amplitude terms in the objective function. In this report we will discuss the algorithm and its theoretical properties. We will also present applications for modeling of subsurface contaminant transport and high-field magnet design.

Keywords

Microwave GaAs Copper Silver 

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References

  1. [1]
    D. Bertsekas; On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Autom. Cont. 21, 1976, 174–184.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. Conn, N. Gould, and P. Toint; LANCELOT: a fortran package for large-scale nonlinear optimization (Release A), in Springer Series in Computational Mathematics No. 17, Springer, Berlin, 1992.MATHGoogle Scholar
  3. [3]
    J. Dennis and R. Schnabel; Numerical Methods for Nonlinear Equations and Unconstrained Optimization, Prentice-Hall, Englewood Cliffs, 1983.MATHGoogle Scholar
  4. [4]
    J. Dennis and V. Torczon; Direct search methods on parallel machines, SIAM J. Optim 1, 1991, 448–474.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Y. Eyssa; Electro-magnetic and temperature analysis of pulsed magnets, to appear in Proc. 14th International Conference on Magnet Technology, 1995.Google Scholar
  6. [6]
    A. Fiacco and G.. McCormick; Nonlinear Programming, Wiley, New York, 1968.MATHGoogle Scholar
  7. [7]
    P. Gilmore; An Algorithm for Optimizing Functions with Multiple Minima, PhD thesis, North Carolina State University, Raleigh, 1993.Google Scholar
  8. [8]
    P. Gilmore; IFFCO: implicit filtering for constrained optimization, Tech. Report CRSC-TR93-7, Center for Research in Scientific Computation, North Carolina State University, Raleigh, 1993. (Available by anonymous ftp from math.ncsu.edu in pub/kelley/iffco/ug.ps.)Google Scholar
  9. [9]
    P. Gilmore and C. Kelley; An implicit filtering algorithm for optimization of functions with many local minima, SIAM J. Optim., to appear.Google Scholar
  10. [10]
    J. Kostrowicki and L. Piela; Diffusion equation method of global minimization: Performance for standard test functions, J. Optim. Theo. Appl. 50, 1991, 269–284.MathSciNetCrossRefGoogle Scholar
  11. [11]
    W. Markiewicz, M. Vaghar, I. Dixon, H. Garmestani, and J. Jimeian, Generalized plane strain analysis of solenoid magnets: Formulation and examples, Tech. Report NHMFLIR 93–788, National High Magnetic Field Laboratory, 1993.Google Scholar
  12. [12]
    D. Mayne and E. Polak; Nondifferential optimization via adaptive smoothing, J. Optim. Theo. Appl. 43, 1984, 601–613.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    C. Miller and F. Cornew; A Petrov-Galerkin method for resolving advective-dominated transport, in Proceedings of Computational Methods in Water Resources IX, Denver, Colorado, Vol. 1 Numerical Methods in Water Resources, Ed. by T. Russell, R. Ewing, C. Brebbia, W. Gray, and G. Pinder, Computational Mechanics Publications, Southhampton and Boston and Elsevier Applied Science, London and New York, 1992, 157–164.Google Scholar
  14. [14]
    C. Miller and A. Rabideau; Development of split-operator, Petrov-Galerkin methods to simulate transport and diffusion problems, Water Resour. Res. 29, 1993, 2227–2240.CrossRefGoogle Scholar
  15. [15]
    D. Montgomery, Solenoid Magnet Design, Krieger, Malabar, 1980.Google Scholar
  16. [16]
    J. Neider and R. Mead; A simplex method for function minimization, Comput. J. 7, 1965, 308–313.Google Scholar
  17. [17]
    J. Ortega and W. Rheinboldt; Iterative Solution of Nonlinear Equations in Several Variables, Academic, New York, 1970.MATHGoogle Scholar
  18. [18]
    D. Stoneking, G. Bilbro, R. Trew, P. Gilmore, and C. Kelley; Yield optimization using a GaAs process simulator coupled to a physical device model, IEEE Trans. Microwave Theo. Tech. 40, 1992, 1353–1363.CrossRefGoogle Scholar
  19. [19]
    D. Stoneking, G.. Bilbro, R. Trew, P. Gilmore, and C. Kelley; Yield optimization using a GaAs process simulator coupled to a physical device model, in Proc. IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE, 1991, 374–383.Google Scholar
  20. [20]
    V. Torczon; On the convergence of the multidimensional direct search, SIAM J. Optim. 1, 1991, 123–145.MathSciNetMATHCrossRefGoogle Scholar
  21. [21]
    V. Torczon; On the convergence of pattern search methods, Tech. Report TR93-10, Department of Computational and Applied Mathematics, Rice University, Houston, 1993.Google Scholar
  22. [22]
    T. Winslow, R. Trew, P. Gilmore, and C. Kelley; Doping profiles for optimum class B performance of GaAs mesfet amplifiers, in Proc. IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE, 1991, 188–197.Google Scholar
  23. [23]
    T. Winslow, R. Trew, P. Gilmore, and C. Kelley; Simulated performance optimization of GaAs MESFET amplifiers, in Proc. IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, [EEE, 1991, 393–402.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • P. Gilmore
    • 1
  • C. T. Kelley
    • 2
  • C. T. Miller
    • 3
  • G. A. Williams
    • 3
  1. 1.National High Magnetic Field LaboratoryFlorida State UniversityTallahasseeUSA
  2. 2.Center for Research in Scientific Computation and Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of Environmental Sciences and EngineeringUniversity of North CarolinaChapel HillUSA

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