The present paper shows how the linear independence constraint qualification (LICQ) can be combined with some conditions put on the first-order and second-order derivatives of the objective function and the constraint functions to ensure the Robinson stability and the Lipschitz-like property of the stationary point set map of a general C²-smooth parametric constrained optimization problem. So, a part of the results in two preceding papers of the authors [J. Optim. Theory Appl. 180 (2019), 91–116 (Part 1); 117–139 (Part 2)], which were obtained for a problem with just one inequality constraint, now has an adequate extension for problems having finitely many equality and inequality constraints. Our main tool is an estimate of B. S. Mordukhovich and R. T. Rockafellar [SIAM J. Optim. 22 (2012), 953–986; Theorem 3.3] for a second-order partial subdifferential of a composite function. The obtained results are illustrated by three examples.

本文展示了如何将线性独立约束限定（LICQ）与目标函数和约束函数的一阶和二阶导数上的一些条件相结合，以确保Robinson稳定性和Lipschitz类性质。一般C ²的固定点集图平滑参数约束优化问题。因此，部分结果来自作者的前两篇论文[J. 最佳 理论应用 180（2019），91–116（Part 1）; 117–139（第2部分）]是针对仅具有一个不等式约束的问题而获得的，现在已经对具有有限多个等式和不等式约束的问题进行了适当的扩展。我们的主要工具是对BS Mordukhovich和RT Rockafellar [SIAM J. Optim。22（2012），953–986；定理3.3]是复合函数的二阶偏亚微分。所获得的结果通过三个例子说明。