Differentiability of projections onto cones and sensitivity analysis for optimal control
Kazimierz Malanowski · 2003
The differentiability properties of the metric projections on the cones of nonnegative functions are considered. It is shown that the metric projection mapping is Bouligand differentiable in L/sup p/(0, 1), but it is not Bouligand differentiable in W/sup 1,p/(0, 1). Using differentiability in L/sup p/(0, 1) the application of Robinson's implicit function theorem for nonsmooth equations to sensitivity analysis for optimal control problems is presented.