两个凸紧集的差及Clarke广义Jacobi与拟微分的关系

Difference for Two Convex Compact Sets and the Relation Between Clarke Generalized Jacobi and Quasidifferential

将 Rn空间中两个凸紧集的 Demyanov差推广到 Rm× n空间 .借助于这种差 ,建立了 Clarke广义 Jacobi与拟微分的关系 ,从而给出了利用拟微分计算 Clarke广义 Jacobi的方法 .对于两个有限点集凸包给出了它们 Demyanov差的具体表达式 .

Demyanov difference for two convex compactsets in R\+n is generalized to R\+\{m×n\}. Using this difference, the relation between Clarke generalized Jacobi and quasidifferential is established. Thus, a method of calculating several elements of Clarke generalized Jacobi via quasidifferential is developed. A formula of the difference for the two sets, which are convex hulls of a finite number of points, is proposed. Finally, the applications to the methods of solving nonsmooth equations are discussed.