A theory of generalized gradients for a general class of functions is developed, as well as a corresponding theory of normals to arbitrary closed sets. It is shown how these concepts subsume theâ€¦ (More)

A subset X of a real Hilbert space H is said to be proximally smooth provided that the function d X : H ! R (the distance to X) is continuously diierentiable on an open tube U around X. It is provenâ€¦ (More)

In this paper, we present new partial subdifferentiation formulas in nonsmooth analysis, based upon the study of two directional derivatives. Simple applications of these formulas include a newâ€¦ (More)

Consider a mapping F from a Hilbert space H to the subsets of H which is upper semicontinuous/Lipschitz, has nonconvex, noncompact values and satisfies to a linear growth condition. We give necessaryâ€¦ (More)

For a closed target set S âŠ‚ R and a control system (formulated as a differential inclusion and defined near S), the present paper considers a sufficient condition for the property that every pointâ€¦ (More)

An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given Îµ > 0, produces Îµ-optimal trajectories thatâ€¦ (More)

First optimality conditions and first existence results in the calculus of variations have been separated in time by more than a century. The formalism based on EulerLagrange equation deals with aâ€¦ (More)

This paper provides necessary conditions of optimality, in the form of a maximum principle, for a broad class of hybrid optimal control problems, in which the dynamics of the constituent processesâ€¦ (More)

Some patients suffering from the same neuropsychiatric disorder may have no overlapping symptoms whilst others may share symptoms common to other distinct disorders. Therefore, the Research Domainâ€¦ (More)