Banach空间集值映射的度量正则性与变分方程的Lipschitz稳定性(英文)

Metric Regularity of Set-valued Mappings and Lipschitzian Stability of Variational Equation in Banach Spaces

综述了集值映射的某些概念,例如度量正则性、伪Lipschitz性质(Aubin性质)、度量次正则性和Calm性质和这些概念的相互关系以及某些判据.也给出了他们在变分方程解的鲁棒Lipschitz稳定性、约束优化问题的最优性条件、集合族的线性正则性质和广义方程迭代过程的收敛性.

In this paper, we survey some concepts for set-valued mappings, such as metric regularity, pesudo-Lipschitz property （or Aubin property）, metric subregularity, and calmness, relationships among these concepts, and some criteria for them. We also present their applications to the robust Lipschitzian stability of solution mappings to variational equations, optimality condition of constrained optimization problems, linear regularity of sets, and convergence of iterative processes for generalized equations.