Using analytic center and cutting planes methods for
nonsmooth convex programming
P. R. Oliveira and M. A. dos Santos
We propose a method for unconstrained minimization of
nondifferentiable convex functions. At each iteration, the algorithm
includes a reinitialization procedure, due to a knew cut, and some
iterations of the analytic center method, those necessary to lower the
upper bound of the best iterate function value. The convergence and
the polynomial complexity by iteration are established, and numerical
tests with typical problems from the literature are presented. The
results are similar to those obtained by bundle methods and the
algorithms that use analytic center.
Submitted to Lecture Notes in Economics and
Mathematical Sciences, V. H. Nguyen, J. J. Strodiot and
P. Tosssings, ed.