Equivalence among various derivatives and subdifferentials of the distance function

Subgradients of Distance Functions at Out-of-Set Points

“…13,15,16,19,21] among other publications devoted to computing and estimating various subgradient sets for the classical distance function (1.1) in finite and infinite dimensions. Note that there are two principal and essentially different cases for generalized differentiation of ( 1.1): the in-set case of x E l1 and the out-of-set case of x ~ l1.…”

Equivalence among various generalized derivatives and generalized subdifferentials of functions defined on binormed spaces

“…2 )-strictly Taylor differentiable at a point x if there exists a continuous linear operator from (E, . 2 ) to (Y, . ) denoted ∇h(x) such that for each v, the following holds: …”

“…Note that V is compact in (E, . 2 ), so that by definition of ∇h(x) for any ε there exists n 0 such that, for all n ≥ n 0 , for all v ∈ V , one has…”

“…Let V any compact subset of (E, . 2 ) and ε any positive number. In view of (ii), there exists for each v in V a number δ(v) such that …”

Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

“…The readers are referred to [4,5,8,9,12,14,15,17,19,21,22,25,26] and the references therein for the study of the minimal time function as well as its specification to the case of the distance function.…”