Nonmonotone trust-region methods for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems

We develop and analyze a class of trust-region methods for bound-constraine d semi-smooth systems of equations. The algorithm is based on a simply cons trained differentiable minimization reformulation. Our global convergence r esults are developed in a very general setting that allows for nonmonotonic ity of the function values at subsequent iterates. We propose a way of comp uting trial steps by a semi-smooth Newton-like method that is augmented by a projection onto the feasible set. Under a Dennis-More-type condition we p rove that close to a regular solution the trust-region algorithm turns into this projected Newton method, which is shown to converge locally q-superli nearly or quadratically, respectively, depending on the quality of the appr oximate subdifferentials used. As an important application we discuss how the developed algorithm can be u sed to solve nonlinear mixed complementarity problems (MCPs). Hereby, the M CP is converted into a bound-constrained semi-smooth equation by means of a n NCP-function. The efficiency of our algorithm is documented by numerical results for a subset of the MCPLIB problem collection.