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 subproblem 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.