  In this paper, a restricted memory quasi-Newton bundle method for minimizing
a locally Lipschitz function over a Riemannian manifold is proposed, which
extends the classical one in Euclidean spaces to the manifold setting. The
curvature information of the objective function is approximated by applying the
Riemannian version of the quasi-Newton updating formulas. The subgradient
aggregation technique is used to avoid solving the time-consuming quadratic
programming subproblem when calculating the candidate descent direction.
Moreover, a new Riemannian line search procedure is proposed to generate the
stepsizes, and the process is finitely terminated under a new version of the
Riemannian semismooth assumption. Global convergence of the proposed method is
established: if the serious iteration steps are finite, then the last serious
iterate is stationary; otherwise, every accumulation point of the serious
iteration sequence is stationary. Finally, some preliminary numerical results
show that the proposed method is efficient.
