Desirability functions of Derringer and Suich, one of the widely used approaches in multiresponse optimization, have nondifferentiable points in their formulations as a drawback. To solve the optimization problem of the overall desirability function, one way is to modify the individual desirability functions by approximation approaches and then to use the gradient based methods. Another way is to use the optimization techniques that do not employ the derivative information. In this study, we propose a new approach which is easy to implement and does not need assumptions like convexity and smoothness. Our approach is based on writing the optimization problem of the overall desirability function as a mixed-integer nonlinear problem, and then putting a constraint on the integer variable to obtain a continuous formulation. The resulting problem is solved as a nonlinear model with discontinuous first order derivatives (DNLP) with Branch And Reduce Optimization Navigator (BARON), a new solver of the General Algebraic Modeling System (GAMS) for nonconvex optimization problems. The solutions obtained for two example problems are better than those of the others.