Restricted Step and Levenberg-Marquardt Techniques in Proximal Bundle Methods for Nonconvex Nondifferentiable Optimization

Two methods are given for minimizing locally Lipschitzian upper semidifferentiable functions. They employ extensions of restricted step (trust region) and Levenberg–Marquardt techniques that are widely used in other contexts. Extensions to linearly constrained optimization are discussed. Preliminary numerical experience is reported.