论文标题
在宽松的恒定正线性依赖性约束条件下，设定值映射的R-RE-RER-RE-RERCOLATY与参数优化的应用和二重优化的应用
R-regularity of set-valued mappings under the relaxed constant positive linear dependence constraint qualification with applications to parametric and bilevel optimization
论文作者
论文摘要
在稳定性分析或双层优化的背景下，希望存在与非线性参数优化问题相关的LIPSchitzian特性用于与非线性参数优化问题相关的解决方案映射。 R-Regulactor性是一种用于设定值映射的Lipschitzian属性的示例，其图是非线性不等式和方程式系统的解决方案集。基于所谓的松弛恒定正线性约束资格，我们提供了一个标准，以确保存在R-Regormulity属性。在这方面，我们的分析概括了这种类型的早期结果，该结果利用了更强大的Mangasarian-Fromovitz或恒定的等级约束资格。之后，我们应用我们的发现来得出新的足够条件，以保证存在参数优化中解决方案映射的R-Regulactor度。最后，我们的结果用于在悲观的二线优化中得出解决方案的存在标准，并有足够的条件，可以在乐观的双层优化中存在所谓的部分平静属性。
The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian-Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.
