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On conditions for optimality in least pth approximation withp → ∞

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Abstract

This paper presents a theoretical discussion of the necessary and sufficient conditions for optimality in generalized nonlinear leastpth approximation problems forp → ∞. In the limit, the conditions for a minimax approximation are derived, as is to be expected. Numerical examples involving the modeling of a linear time-invariant fourth-order system by a second-order model and the design of quarter-wave transmission-line transformers illustrate the results.

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References

  1. Dem'yanov, V. F.,Sufficient Conditions for Local Minimax, Zh. Vychisl. Mat. Fiz., Vol. 10, No. 5, 1970.

  2. Medanic, J.,Solution of the Convex Minimax Problem by the Newton-Raphson Method, Proceedings of the 8th Annual Allerton Conference on Circuit and System Theory, Urbana, Ill., 1970.

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  4. Temes, G. C., andZai, D. Y. F.,Least pth Approximation, IEEE Transactions on Circuit Theory, Vol. CT-16, No. 2, 1969.

  5. Bandler, J. W., andCharalambous, C.,Theory of Generalized Least pth Approximation, IEEE Transactions on Circuit Theory, Vol. CT-19, No. 3, 1972.

  6. Bandler, J. W.,Optimization Methods for Computer-Aided Design, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-17, No. 8, 1969.

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  8. Bandler, J. W., andCharalambous, C.,Practical Least pth Approximation with Extremely Large Values of p, Conference Record of the 5th Asilomar Conference on Circuits and Systems, Pacific Grove, Calif., 1971.

Additional Bibliography

  1. Bandler, J. W., andMacDonald, P. A.,Cascaded Noncommensurate Transmission-Line Networks as Optimization Problems, IEEE Transactions on Circuit Theory, Vol. CT-16, No. 3, 1969.

  2. Bandler, J. W., andMacDonald, P. A.,Optimization of Microwave Networks by Razor Search, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-17, No. 8, 1969.

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Authors and Affiliations

  1. Department of Electrical Engineering, McMaster University, Hamilton, Ontario, Canada

    J. W. Bandler (Associate Professor of Electrical Engineering)

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    C. Charalambous (Postdoctoral Fellow)

Authors
  1. J. W. Bandler
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  2. C. Charalambous
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Additional information

Communicated by C. T. Leondes

This work was supported by the National Research Council of Canada under Grant No. A7239 and by a Frederick Gardner Cottrell Grant from the Research Corporation. This paper was presented at the 9th Annual Allerton Conference on Circuit and System Theory, Urbana, Illinois, October 6–8, 1971. The authors thank Mrs. J. R. Popović for helping to correct Example 4.1.

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Bandler, J.W., Charalambous, C. On conditions for optimality in least pth approximation withp → ∞. J Optim Theory Appl 11, 556–566 (1973). https://doi.org/10.1007/BF00935666

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  • DOI: https://doi.org/10.1007/BF00935666

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