A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization

Proximal bundle method has usually been presented for unconstrained convex optimization problems. In this paper, we develop an infeasible proximal bundle method for nonsmooth nonconvex constrained optimization problems. Using the improvement function we transform the problem into an unconstrained one and then we build a cutting plane model. The resulting algorithm allows effective control of the size of quadratic programming subproblems via the aggregation techniques. The novelty in our approach is that the objective and constraint functions can be any arbitrary (regular) locally Lipschitz functions. In addition the global convergence, starting from any point, is proved in the sense that every accumulation point of the iterative sequence is stationary for the improvement function. At the end, some encouraging numerical results with a MATLAB implementation are also reported.