A NEW PROXIMAL CHEBYCHEV CENTER CUTTING PLANE ALGORITHM FOR NONSMOOTH OPTIMIZATION AND ITS CONVERGENCE

摘要

Motivated by the proximal-like bundle method [K. C. Kiwiel, Journal of Optimization Theory and Applications, 104(3) (2000), 589-603.], we establish a new proximal Chebychev center cutting plane algorithm for a type of nonsmooth optimization problems. At each step of the algorithm, a new optimality measure is investigated instead of the classical optimality measure. The convergence analysis shows that an epsilon-optimal solution can be obtained within O (1/epsilon(3)) iterations. The numerical result is presented to show the validity of the conclusion and it shows that the method is competitive to the classical proximal-like bundle method.