This paper concerns saddle points of rational functions, under general constraints. Based on optimality conditions, we propose an algorithm for computing saddle points. It uses Lasserre’s hierarchy of semidefinite relaxation. The algorithm can get a saddle point if it exists, or it can detect its nonexistence if it does not. Numerical experiments show that the algorithm is efficient for computing saddle points of rational functions.

中文翻译：

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有理函数的鞍点

本文涉及一般约束下有理函数的鞍点。基于最优条件，我们提出了一种计算鞍点的算法。它使用Lasserre的半确定松弛层次。该算法可以获取一个鞍点（如果存在），或者可以检测到它的不存在（如果不存在）。数值实验表明，该算法对于计算有理函数的鞍点是有效的。