We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where the constraint qualifications fail and extra work for other methods becomes inevitable. This method also serves as a tool to calculate the regular co-derivative for semismooth* Newton methods. We list algorithms and their demonstrations of different use cases for this approach.

翻译：我们提出了利用量词消去计算正则法锥及相关对象的有效程序。这种法锥计算方法与拉格朗日方法互补，在约束规格失效且其他方法必须进行额外计算的点上表现最佳。该方法还可用于计算半光滑*牛顿方法中的正则余导数。我们列出了该方法的算法及其在不同应用场景中的演示。