Nonsmooth Analysis on Smooth Manifolds
We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function.
A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.
WMU ScholarWorks Citation
Ledyaev, Yu. S. and Zhu, Qiji Jim, "Nonsmooth Analysis on Smooth Manifolds" (2007). Math Faculty Publications. 34.