This study establishes the convergence of a cutting-plane algorithm tailored for a specific non-convex optimization problem. The presentation begins with the problem definition, accompanied by the necessary hypotheses that substantiate the application of a cutting plane. Following this, we develop an algorithm designed to tackle the problem. Lastly, we provide a demonstration that the sequence generated by the algorithm converges to a solution to the problem. To illustrate the convergence of the algorithm visually, numerical experiments are conducted using Matlab.