An entropic regularized method of centers for continuous minimax problem with semi infinite constraints

The purpose of this paper is to focus on continuous minimax problems with semi infinite constraints. We begin by proposing an algorithm for solving this kind of problems. The proposed algorithm combines the parametric approach and the Huard method of centers. That's we extend the Method of Centers of Roubi for solving minimax fractional programs to continuous minimax problems. On the other hand, calculating the exact optimal solution of the proposed parametric problems, requires an extraordinary computational work per iteration. To overcome this problem we use an iterative entropic regularization method which allows us to solve each auxiliary problem inexactly generating an approximate sequence of optimal values and then the continuous minimax problem is reduced into a sequence of finite minimax problems. Examples for illustration are given to test our algorithm.