A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization

By using the Moreau-Yosida regularization and proximal method, a new trust region algorithm is proposed for nonsmooth convex minimization. A cubic sub-problem with adaptive parameter is solved at each iteration. The global convergence and Q-superlinear convergence are established under some suitable conditions. The overall iteration bound of the proposed algorithm is discussed. Preliminary numerical experience is reported.