Nonconvex Quasi-Variational Inequalities: Stability Analysis and Application to Numerical Optimization
研究了无凸性假设的参数化拟变分不等式，通过最优值函数转化为非光滑不等式系统，推导了新的余导数估计和稳定性条件，并设计了半光滑牛顿方法求解带QVI约束的优化问题，数值实验验证了有效性。
Abstract We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of optimal value function , we transform the problem into that of solving a nonsmooth system of inequalities. Based on this reformulation, new coderivative estimates as well as robust stability conditions for the optimal solution map of this QVI are developed. Also, for an optimization problem with QVI constraint, necessary optimality conditions are constructed and subsequently, a tailored semismooth Newton-type method is designed, implemented, and tested on a wide range of optimization examples from the literature. In addition to the fact that our approach does not require convexity, its coderivative and stability analysis do not involve second order derivatives, and subsequently, the proposed Newton scheme does not need third order derivatives, as it is the case for some previous works in the literature.