Abstract:

A hybrid bundle method for nonsmooth convex optimization problems is proposed. In this method, the next iterate point is obtained by solving a subproblem which is formed by adding proximal term to the objective function and trust region constraint to the feasible region. The proposed algorithm combines proximal bundle method with trust region bundle method and switches between them automatically. Convergence analysis shows that the algorithm we proposed is global convergent. Finally, a numerical example is given to verify the validity of the method we proposed.

Key words: nonsmooth optimization, proximal bundle method, trust region bundle method