Lower Semicontinuity of Multivalued Linearization Mappings
Stephen M. Robinson, Robert R. Meyer · SIAM Journal on Control · 1973
Many results in mathematical programming require lower semicontinuity of the multi-valued function obtained from a constraint set by replacing the functions defining the set by their linearizations about a point. In this paper we give a simple sufficient condition, involving the gradients of the active linearized constraints, for this property to hold. We further show that this is the weakest possible condition which uses only first order information at the point in question.