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.

本文的目的是关注具有半无限约束的连续极小极大问题。我们首先提出一种解决此类问题的算法。所提出的算法结合了参数方法和中心的Huard方法。那就是我们将用于解决极小极大分数程序的鲁比中心方法扩展到了连续极小问题。另一方面，计算所提出的参数问题的精确最佳解决方案，则每次迭代都需要大量的计算工作。为了克服这个问题，我们使用迭代熵正则化方法，该方法允许我们解决每个辅助问题，从而不精确地生成最佳值的近似序列，然后将连续极小值问题简化为有限极小值问题的序列。