A second order bundle algorithm for nonsmooth, nonconvex optimization problems

In this chapter we extend the SQP-approach of the well-known bundle- Newton method for nonsmooth unconstrained minimization and the second order bundle method by Fendl and Schichl (A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. derivation and convergence. arXiv:1506.07937, 2015, preprint) to the general nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with the presence of constraints, the search direction is determined by solving a convex quadratically constrained quadratic program to obtain good iteration points. Furthermore, global convergence of the method is shown under certain mild assumptions.