A parallel implementation of the ALOPEX process

Optimization techniques have found many applications in science, engineering, and industry. In all applications, the best value of a "cost function" is sought in a well-defined domain; this cost function in general depends on many parameters. An iterative optimization technique has been developed (ALOPEX) that uses feedback in order to optimize the response of a system. The cost function for this process is problem dependent and therefore quite flexible. The method has been applied successfully to different optimization problems such as pattern recognition, receptive field studies in the visual system of animals, curve fitting, etc. We present two special purpose hardware implementations for ALOPEX. The first method takes time O(logN + logm) and uses O(mN2) processing elements. The second method takes O(logN + m) time and uses O(N2) processing elements. Our basic architecture is a binary tree with N2 leaves (equal to the length of the vectors) and therefore had depth O(logN). Different implications of the two approaches will be discussed including similarities with the biological visual process.