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This paper extends the SQP-approach of the well-known bundle-Newton methodfor nonsmooth unconstrained minimization to the nonlinearly constrained case.Instead of using a penalty function or a filter or an improvement function todeal with the presence of constraints, the search direction is determined bysolving a convex quadratically constrained quadratic program to obtain gooditeration points. Issues arising with this procedure concerning the bundlingprocess as well as in the line search are discussed. Furthermore, globalconvergence of the method is shown under certain mild assumptions.

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