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

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3 Author(s)
Jelonek, T.M. ; Commun. Res. Lab., McMaster Univ., Hamilton, Ont., Canada ; Reilly, J.P. ; Qiang Wu

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

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Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:42 ,  Issue: 4 )