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 and used for reformulation of black-box objective functions as continuous functions. Particle swarm optimization (PSO) was then applied to locate the global optimal solutions of the continuous functions derived. The continuous functions generated by the proposed. discrete Fourier series method correlated almost exactly with their original black-box counterparts. The PSO algorithm was observed to be highly successful in achieving global optimization of all such objective functions considered in this study. Case studies were also carried out in which the methodology developed here was applied to the optimization of the formulation for culture media used for cultivating a freshwater microalga, Haematococcus pluvialis, as well as for a one-dimensional regression problem. Subsequently, the methodology was extended to solving a two-dimensional black-box optimization problem that was simulated based on the Rosenbrock function. The possibility of applying the same approach for solving the chemical plume tracing problem in the area of chemical defense was also successfully demonstrated. The results obtained indicate that the discrete Fourier series method coupled with the PSO algorithm is indeed a promising methodology for solving black-box optimization problems by a continuous approach.