<p>In this study, we present the different aspects of functional properties of desirability functions which is a scalarization method for multi-response optimization problems (MROPs). In a multiple-response optimization problem, the aim is to define and achieve the optimal conditions for a process, product or system by considering multiple response variables simultaneously. Desirability functions is currently a well-known and powerful tool for researchers and scientist who study MROPS. The paper presents a study on the mathematical analysis of desirability functions focusing on two key aspects: Lipschitz continuity and Clarke generalized derivative. The paper highlights the importance of understanding the mathematical properties of desirability functions in decision-making and optimization. The findings of the paper have implications for the development of optimization algorithms and strategies for handling nonsmooth functions. We end with a conclusion and an outlook to future researches and applications. </p>