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This paper presents a concrete implementation of the feasible second orderbundle algorithm for nonsmooth, nonconvex optimization problems with inequalityconstraints \cite{HannesPaperB}. It computes the search direction by solving aconvex quadratically constrained quadratic program. Furthermore, certainversions of the search direction problem are discussed and the applicability ofthis approach is justified numerically by using different solvers for thecomputation of the search direction. Finally, the good performance of thesecond order bundle algorithm is demonstrated by comparison with test resultsof other solvers on examples of the Hock-Schittkowski collection, on customexamples that arise in the context of finding exclusion boxes for quadraticconstraint satisfaction problems, and on higher dimensional piecewise quadraticexamples.

A feasible second order bundle algorithm for nonsmooth nonconvex  optimization problems with inequality constraints: II. Implementation and  numerical results