Nonsmooth analysis on smooth manifolds

By Yu. S. Ledyaev, Qiji Jim Zhu. 2007

135 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/cdabfa9e6ee018213479f0ee0170ce7d3cdd112c

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In Computational Theory and Mathematics

In Mechanics of Materials

Alexandru Krist'aly

Citations in the corpus

Monotone and Accretive Vector Fields on Riemannian Manifolds (2010, background): “On the other hand, various derivative-like and subdifferential constructions for nondifferentiable functions on spaces with nonlinear structure have been developed and applied to the study of constrained optimization problems, nonclassical problems of the calculus of variations and optimal control; ”
Nash-type equilibria on Riemannian manifolds: a variational approach (2016, methodology): “3 [23] Let (M, g) be a finite-dimensional Riemannian manifold and let f :M → R ∪ {+∞} be a lower semicontinuous function.”
Proximal point method for a special class of nonconvex functions on Hadamard manifolds (2008, background): “Severalworks have studied such concepts and presented many useful results in the Riemannian optimization context; see for example [17,5,18,19].”