Abstract. 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 Φ : T M → R on the tangent bundle T M , and at k-th iteration, using the restricted function Φ| Tx k M where Tx k M is the tangent space at x k , a local model function Q k 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 ε-subdifferential, a suitable model function is defined. Numerical experiments illustrate our results.
Grohs REF presented a nonsmooth trust region algorithm for minimizing locally Lipschitz objective function on Riemannian manifold.
Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds
Ima Journal of Numerical Analysis
Mathematics