A Triple Stabilized Bundle Method for Constrained Nonconvex Nonsmooth Optimization

In this paper, we provide an exact reformulation of Nonsmooth Constrained optimization Problems (NCP) using the Moreau-Yosida regularization. This reformulation allows the transformation of (NCP) to a sequence of convex programs of which solutions are feasible for (NCP). This sequence of solutions of auxiliary programs converges to a local solution of (NCP). Assuming Slater constraint qualification and basing on an exact penalization, our reformulation combined with a nonconvex proximal bundle method provides a local solution of (NCP). Our bundle method allows a strong update of the level set, may reduce significantly the number of null-steps and gives a new stopping criterion. Finally, numerical simulations are carried out.