Nonsmooth Trust Region Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
نویسندگان
چکیده
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 : TM → R on the tangent bundle TM , and at k-th iteration, using the restricted function Φ|TxkM where TxkM is the tangent space at xk, 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 εsubdifferential, a suitable model function is defined. Numerical experiments illustrate our results.
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