Solving Continuous Min-Max Problems by an Iterative Entropic Regularization Method

We propose a method of outer approximations, with each approximate problem smoothed using entropic regularization, to solve continuous min-max problems. By using a well-known uniform error estimate for entropic regularization, convergence of the overall method is shown while allowing each smoothed problem to be solved inexactly. In the case of convex objective function and linear constraints, an interior-point algorithm is proposed to solve the smoothed problem inexactly. Numerical examples are presented to illustrate the behavior of the proposed method.