Real-time, analog, global optimization with constraints: Application to the direction of arrival estimation problem

IEEE Trans. CAS-II, Vol. 42,No. 4. Apr. 1995, pp. 233-244
J. Reilly and T. Jelonek

Abstract   An analog technique for real­time, multi­variate, global optimization with constraints is presented. The basic structure is a simple gradient descent loop, where the gradients are computed using an analog neural network. Constraints are implemented using a variation of an idea due to [17], where neural networks are also used to implement the required constraint functions. It is shown that the system converges to a stable equilibrium point, which satisfies the Kuhn­Tucker conditions for a constrained minimum. Global optimization is achieved by introducing a diffusion process into the governing differential equation. This procedure is a continuous­time analog of the simulated annealing algorithm. Even though the proposed method is applicable to a wide range of engineering problems, the real­time, global and other capabilities of this method are demonstrated specifically with an optimization problem from array signal processing ­ the maximum likelihood direction of arrival estimator. The satisfactory performance of all aspects of this proposed optimization technique is demonstrated by simulations.