论文标题
非convex准变量不平等：稳定性分析和用于数值优化的应用
Nonconvex quasi-variational inequalities: stability analysis and application to numerical optimization
论文作者
论文摘要
我们考虑没有任何凸度假设的参数准变量不平等（QVI）。使用\ emph {最佳值函数}的概念，我们将问题转换为解决不平等系统的非平滑系统的问题。基于此重新制定，开发了该QVI最佳解决方案图的新代码估计以及稳健的稳定性条件。同样，对于QVI约束的优化问题，构建了必要的最佳条件，随后，在文献中设计，实现和测试了量身定制的半齿牛顿型方法。除了我们的方法不需要凸度的事实外，其代码和稳定性分析不涉及二阶导数，随后，提出的牛顿方案不需要三阶衍生物，因为文献中某些以前的作品就是这种情况。
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of \emph{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.
