It is proved that the upper subderivative of a lower semicontinuous function on a Banach space is upper semicontinuous for the first variable as x′→f x, i. e., x′-x, f(x′)-f(x). By taking account of the work of Tr...It is proved that the upper subderivative of a lower semicontinuous function on a Banach space is upper semicontinuous for the first variable as x′→f x, i. e., x′-x, f(x′)-f(x). By taking account of the work of Treiman. it is further shown that the upper subderivative of a 1. s. c. function is the upper limit of the contingent directtional derivatives around the concorned point. This new characterization of the upper suoberivative allows simple derivations and natural extension of many results' in nonsmooth analysis.展开更多
We give a new characterization of the paratingent cone in terms of contingent cones,i. e., the paratingent cone to any open set at a boundary point is the upper limit of the contingentcones at the neighboring points. ...We give a new characterization of the paratingent cone in terms of contingent cones,i. e., the paratingent cone to any open set at a boundary point is the upper limit of the contingentcones at the neighboring points. We use this result to characterize the strict differentiability in termsof the contingent directional derivatives. We also define a P-subderivative for continuous functionsand develop a subdifferential calculus with applications to optimality conditions in mathematicalprograming.展开更多
文摘It is proved that the upper subderivative of a lower semicontinuous function on a Banach space is upper semicontinuous for the first variable as x′→f x, i. e., x′-x, f(x′)-f(x). By taking account of the work of Treiman. it is further shown that the upper subderivative of a 1. s. c. function is the upper limit of the contingent directtional derivatives around the concorned point. This new characterization of the upper suoberivative allows simple derivations and natural extension of many results' in nonsmooth analysis.
文摘We give a new characterization of the paratingent cone in terms of contingent cones,i. e., the paratingent cone to any open set at a boundary point is the upper limit of the contingentcones at the neighboring points. We use this result to characterize the strict differentiability in termsof the contingent directional derivatives. We also define a P-subderivative for continuous functionsand develop a subdifferential calculus with applications to optimality conditions in mathematicalprograming.
