This paper is concerned with the computation of perfect stationary point, which is a strict refinement of stationary point. A differentiable homotopy method is developed for finding perfect stationary points of continuous functions on convex polytopes. We constitute an artificial problem by introducing a continuously differentiable function of an extra variable. With the optimality conditions of this problem and a fixed point argument, a differentiable homotopy mapping is constructed. As the extra variable becomes close to zero, the homotopy path naturally provides a sequence of closely approximate stationary points on perturbed polytopes, and converges to a perfect stationary point on the original polytope. Numerical experiments are implemented to further illustrate the effectiveness of our method.

中文翻译：

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一种计算完美静止点的微分路径跟踪算法

本文涉及完美定点的计算，这是对定点的严格改进。开发了一种可微分同伦方法，以找到凸多面上的连续函数的完美平稳点。通过引入额外变量的连续可微函数，我们构成了一个人为的问题。利用该问题的最优条件和不动点参数，构造了可微同伦映射。当额外变量接近于零时，同构路径自然会在扰动的多态上提供一系列紧密近似的固定点，并收敛到原始多态上的理想固定点。进行数值实验以进一步说明我们方法的有效性。