Non-Convex Quadratic Programming Problems in Short Wave Antenna Array Optimization

In this paper, we describe a non-convex constrained quadratic programming problem arising in short wave transmitting antenna array synthesis and provide preliminary computational results. We consider problem instances for three different antenna designs including up to 25 radiators. In the computational experiments, BARON package is compared to the gradient optimization method, applied to the unconstrained problem formulation using the penalty function method. Global optimality of the obtained solutions is established using BARON package the smallest instances of 4 radiators. On small instances, both methods have demonstrated similar results, while on larger instances significant difference has been observed. The set of local optima is studied experimentally. It is established that even though the problem instances have numerous local optima, the objective function in many local optima has the same value.