The traditional method for determining a periodic state (cyclic steady state) of a mathematical model of an adsorption cycle involves simulating a process through successive cycles until the solution is not changing significantly from cycle to cycle. Optimization is then carried out by exploring the solution space by varying parameters and determining several periodic states until an optimum or near-optimum solution is found. This paper introduces an alternative method for determining the optimum periodic state of an adsorption cycle. The approach is based on our method for determining a periodic state directly rather than by simulating successive cycles (Chem. Eng. Sci. 49 (1994a) 1821). For optimization, we introduce an objective function into the equation set. The error in minimizing this objective function is driven to zero at the same time that errors in meeting the periodicity requirement and constraints are driven to zero. Thus, the first periodic state found is an optimum one. Examples are given of optimization of a temperature swing adsorption cycle and a pressure swing adsorption cycle. Simulation results show that the new approach is an efficient method for periodic state optimization. An optimum feed temperature is found for the temperature swing adsorption cycle.