A new computational method for the functional inequality constrained minimax optimization problem

Considers a general class of functional inequality constrained minimax optimisation problems. This problem is first converted into a semi-infinite programming problem. Then, an auxiliary cost function is constructed based on a positive saturated function. The smallest zero of this auxiliary cost function is equal to the minimal cost of the semi-infinite programming problem. However, this auxiliary cost function is non-smooth. Thus, a smoothing function is introduced. Then, an efficient computational procedure is developed for approximating the smallest zero of this auxiliary cost function. Furthermore, an error bound is established to validate the accuracy of the approximate solution. For illustration, two numerical examples are solved using the proposed approach