A Second Order Smooth Variational Principle on Riemannian Manifolds

A Second Order Smooth Variational Principle on Riemannian Manifolds

We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.

Stochastic variational principle on riemannian manifolds

Nonlinear second-order dynamical systems on Riemannian manifolds: Damped oscillators

Linear as well as non-linear mathematical systems that exhibit an oscillatory behavior are ubiquitous in sciences and engineering. Such mathematical systems have been used to model the behavior of biological structures, such as the pulsating contraction of cardiac cells, as well as the behavior of electrical and mechanical components. Chaotic oscillators are currently being used in the secure t...

Variational collision avoidance problems on Riemannian manifolds

In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The problem consists of finding non-intersecting trajectories of a given number of agents, among a set of admissible curves, to reach a specified configuration, based on minimizing an energy functional that depends on the ...

Sufficient Decrease Principle on Riemannian Manifolds

Tools from Riemannian geometry (suitable Riemannian metric, exponential map, search along geodesics, covariant differentiation, sectional curvature, etc) are now used in Mathematical Programming to obtain deeply theoretical results and practical algorithms [3]-[11]. §1 lists basic propositions appearing in the numerical finding of a critical point of a real function defined on a Riemannian mani...