Abstract
In this paper we consider a special optimization problem withtwo objectives which arises in antenna theory. It is shown that thisabstract bicriterial optimization problem has at least one solution.Discretized versions of this problem are also discussed, and therelationships between these finite dimensional problems and the infinitedimensional problem are investigated. Moreover, we presentnumerical results for special parameters using a multiobjectiveoptimization method.
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T.S. Angell and A. Kirsch, "Multicriteria optimization in antenna design," Math. Methods Appl. Sci., vol. 15, pp. 647–660, 1992.
T.S. Angell, A. Kirsch, and R.E. Kleinman, "Antenna control and optimization," Proc. IEEE., vol. 79, pp. 1559–1568, 1991.
T.S. Angell and R.E. Kleinman, "Generalized exterior boundary value problems and optimization for the Helmholtz equation," J. Optim. Theory Appl., vol. 37, pp. 469–497, 1982.
T.S. Angell and R.E. Kleinman, "A Galerkin procedure for optimization in radiation problems," SIAM J. Appl. Math., vol. 44, pp. 1246–1257, 1984.
T.S. Angell, R.E. Kleinman, and A. Kirsch, "Multicriteria optimization in arrays," in Proc. J. Intern. de Nice sur le Antennes, Nice, France, 1992.
R.E. Collin and F.J. Zucker, Antenna Theory, part 1, McGraw-Hill: New York, 1969.
D.L. Colton and R. Kress, Integral Equation Methods in Scattering Theory, J. Wiley: New York, 1983.
J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces, Peter Lang: Frankfurt, Germany, 1986.
J. Jahn and A. Merkel, "Reference point approximation method for the solution of bicriterial nonlinear optimization problems," J. Optim. Theory Appl., vol. 74, pp. 87–103, 1992.
D.S. Jones, Methods in Electromagnetic Wave Propagation, Clarendon Press: Oxford, 1979.
A. Jüschke, "Ein bikriterielles Optimierungsproblem aus der Antennentheorie," Diplom thesis, University of Erlangen-Nürnberg, Erlangen, Germany, 1994.
A. Kirsch and P. Wilde, "The optimization of directivity and signal-to-noise ratio of an arbitrary antenna array", Math. Meth. Appl. Sci., vol. 10, pp. 153–164, 1988.
N.N. Lebedev, Special Functions and Their Applications, Prentice Hall: Englewood Cliffs, 1965.
Y.T. Lo, S.W. Lee, and Q.H. Lee, "Optimization of directivity and signal-to-noise ratio of an arbitrary antenna array," Proc. IEEE, vol. 54, pp. 1033–1045, 1966.
E. Polak, "On the approximation of solutions to multiple criteria decision making problems," in Multiple Criteria Decision Making, M. Zeleny (Ed.), Kyoto, 1975, Springer: Berlin, Germany, pp. 271–281, 1976.
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Jüschke, A., Jahn, J. & Kirsch, A. A Bicriterial Optimization Problem of Antenna Design. Computational Optimization and Applications 7, 261–276 (1997). https://doi.org/10.1023/A:1008611827855
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DOI: https://doi.org/10.1023/A:1008611827855