Robust Solution of Mixed Complementarity Problems

Robust Solution of Mixed Complementarity Problems Steven P Dirkse Under the Supervision of Associate Professor Michael C Ferris at the University of Wisconsin Madison This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem or MCP The MCP formulation is useful for expressing systems of nonlinear inequalities and equations the complementarity allows boundary conditions be to speci ed in a succinct manner Problems of this type occur in many branches of the sciences including mathematics engineering economics operations research and computer science The algorithm we propose for the solution of MCP is a Newton based method containing a novel application of a nonmonotone stabilization technique previously applied to methods for solving smooth systems of equalities and for unconstrained minimization In order to apply this technique we have adapted and extended the path construction technique of Ralph resulting in the PATH algorithm We present a global convergence result for the PATH algorithm that generalizes similar results obtained in the smooth case The PATH solver is a sophisticated implementation of this algorithm that makes use of the sparse basis updating package of MINOS Due to the widespread use of algebraic modeling languages in the practice of operations research economics and other elds from which complementarity problems are drawn we have developed a complementarity facility for both the GAMS and AMPL modeling lan guages as well as software interface libraries to be used in hooking up a complementarity solver as a solution subsystem These interface libraries provide the algorithm developer with