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Optimal design of efficient acoustic antenna arrays.(English)Zbl 0643.49009

The authors describe an optimal design problem in antenna theory. Mathematically it leads to a minimization problem with a linear cost functional, many quadratic inequality constraints and one nonconvex constraint. For the numerical treatment the authors propose to use Lagrangian relaxation with respect to the quadratic constraints only and adjust the multipliers by a steepest ascent method. Examples with up to 391 variables and 579 constraints complete the paper.
Reviewer: A.Kirsch

MSC:

49J35 Existence of solutions for minimax problems
49M37 Numerical methods based on nonlinear programming
78A50 Antennas, waveguides in optics and electromagnetic theory
90C99 Mathematical programming
49M20 Numerical methods of relaxation type
90C20 Quadratic programming
65K10 Numerical optimization and variational techniques

Cite

References:

[1]H. Cox and J. Thurston, ”Advanced conformal submarine acoustic sensor beamforming engineering,” Report No. 5258, Bolt Beranek and Newman, Inc., Suite 400, 1300 N. 17th St., Arlington, VA, 22209, (March 1983).
[2]D.J. Edelblute, J.M. Fisk and G.L. Kinnison, ”Criteria for optimum signal detection theory for arrays,”Journal of the Acoustical Society of America, 41 (1967) 199–205. ·Zbl 0148.40601 ·doi:10.1121/1.1910317
[3]L.S. Lasdon, A.D. Waren and D. Suchman, ”Optimal design of acoustic sonar transducer arrays,”Proceedings of IEEE International Conference on Engineering in the Ocean Environment 1 (1974) 3–10. ·doi:10.1109/OCEANS.1974.1161451
[4]L.S. Lasdon and A.D. Waren, ”Generalized reduced gradient software for linearly and nonlinearly constrained problems,” in: H. Greenberg, ed.,Design and Implementation of Optimization Software (Sijthoff and Noordhoff, 1978) 363–397.
[5]W. Mossberg, ”Quiet defender,” The Wall Street Journal 1 (May 19 1983) 22.
[6]B.A. Murtagh and M.A. Saunders, ”Large-scale linearly constrained optimization,”Mathematical Programming 14 (1978) 41–72. ·Zbl 0383.90074 ·doi:10.1007/BF01588950
[7]J. Plummer, L.S. Lasdon and M. Ahmed, ”Solving a large nonlinear programming problem on a vector processing computer,” Working Paper 85/86-3-1 Department of Management Science and Information Systems, School of Business Administration, University of Texas, Austin, TX 78712 (1985).
[8]D.F. Shanno, ”Conjugate gradient methods with inexact searches,”Mathematics of Operations Research 3 (1977) 241–254.
[9]R.L. Streit and A.H. Nuttall, ”A general chebyshev complex function approximation procedure and an application to beamforming,”Journal of the Acoustical Society of American 72 (1982), 181–190. ·Zbl 0492.65009 ·doi:10.1121/1.388002
[10]A.D. Waren, L.S. Lasdon and D. Suchman, ”Optimization in engineering design,”Proceedings of the IEEE 55 (1967) 1185–1196. ·doi:10.1109/PROC.1967.5777
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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