An efficient version of a numerical gradient optimization procedure for the computation of solutions to periodic optimal control problems is presented. This procedure consists of a first order gradient method in combination with the Newton-Picard shooting method. The first order gradient method is able to compute the optimal control of a periodic process under one or more nonlocal constraints, such as a minimum purity constraint. The Newton-Picard method computes very efficiently periodic solutions to the state and adjoint equations. The presented numerical procedure is used to optimize a rapid pressure swing reactor and a rapid pressure swing adsorber. It is shown that the optimal cycle scheme consists of four steps: a no-inflow pre-pressurization step, a pressurization step, a no-inflow post-pressurization step, and a depressurization step. (C) 2003 Elsevier Ltd. All rights reserved.