A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. Derivation and convergence

This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the 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.