Optimal design of efficient acoustic antenna arrays

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.