A proximal cutting plane method using Chebychev center for nonsmooth convex optimization

An algorithm is developped for minimizing nonsmooth convex functions. This algortithm extends Elzinga-Moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our method is to Elzinga-Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. As in proximal bundle methods, a quadratic problem is solved at each iteration, but the usual polyhedral approximation values are not used. We propose some variants and using some academic test problems, we conduct a numerical comparative study with three other nonsmooth methods. Mathematics Subject Classification (2000) 90C30, 90C25, 65K05