Abstract
Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint. The variables of this problem are a scaling and phase shift applied to the output of each sensor.
This problem is solved by applying Lagrangian relaxation to the convex quadratic constraints.
Extensive computational experience shows that this approach can efficiently find near-optimal solutions of problems with up to 391 variables and 579 constraints.
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This work was supported by ONR Contracts N00014-83-C-0437 and N00014-82-C-824.
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Lasdon, L.S., Plummer, J., Buehler, B. et al. Optimal design of efficient acoustic antenna arrays. Mathematical Programming 39, 131–155 (1987). https://doi.org/10.1007/BF02592949
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DOI: https://doi.org/10.1007/BF02592949