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

An analog technique for real-time, 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, 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 Kuhn-Tucker conditions for a constrained minimum. Global optimization is achieved by introducing a diffusion process into the governing differential equation. This procedure is a continuous-time analog of the simulated annealing algorithm. Even though the proposed method is applicable to a wide range of engineering problems, the real-time, 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