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In this paper we are concerned with a formulation of the Chebyshev approximation problem in the complex plane as a problem of linear optimization in the presence of infinitely many constraints. It is shown that there exist stable and fast algorithms for the solution of optimization problems of this type. Some numerical examples are presented.doi:10.1090/s0025-5718-1981-0595055-4 fatcat:wahylzcee5bobl4k33rd6hnroq