Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds

摘要

This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function Phi : TM -> R, on the tangent bundle TM, and at the kth iteration, using the restricted function Phi/TxkM, where TxkM is the tangent space at x(k), a local model function Qk that carries both first- and second-order information for the locally Lipschitz objective function f :M -> R on a Riemannian manifold M. is defined and minimized over a trust region. We establish the global convergence of the proposed algorithm. Moreover, using the Riemannian e-subdifferential, a suitable model function is defined. Numerical experiments illustrate our results.