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We present an algorithm for finding a nearest pair of points in two convex sets of R n, and therefore, their distance. The algorithm is based on the fixed-point theory of nonexpansive operators on a Hilbert space. Its practical implementation requires a fast projection algorithm. We introduce such a procedure for convex polyhedra. This algorithm effects a local search in the faces using visibility as a guide for finding the global minimum. After studying the convergence of both algorithms, wedoi:10.1016/s0898-1221(00)85008-7 fatcat:sivbnlitarftva33giclaan4yy