A new methodology for solving black-box optimization problems by the continuous approach has been developed in this study. A discrete Fourier series method was derived from the conventional Fourier series formulation and principles associated with the discrete Fourier transform, and used for the reformulation of black-box objective functions as continuous functions. A stochastic global optimization technique known as Particle Swarm Optimization (PSO) was then applied to locate the global optimal solutions of the continuous functions derived. The methodology was first applied to the solution of a black-box optimization problem that was simulated on the basis of the Himmelblau function. It was then applied successfully to the optimization of the conditions used for various types of experiments such as those involving the permeation of nimodipine through human cadaver epidermis, lipid production, and the production of a human interferon beta by the recombinant bacteria Escherichia coli. The discrete Fourier series method coupled to the PSO algorithm is thus a promising methodology for solving black-box optimization problems via the continuous approach.