Complementarity problems in GAMS and the PATH solver

Complementarity problems in GAMS and the PATH solver

A fundamental mathematical problem is to "nd a solution to a square system of nonlinear equations. There are many methods to approach this problem, the most famous of which is Newton's method. In this paper, we describe a generalization of this problem, the complementarity problem. We show how such problems are modeled within the GAMS modeling language and provide details about the PATH solver,...

Mixed Complementarity Programming with GAMS

GAMS (General Algebraic Modelling System) is a computer language which was originally developed to assist economists at the World Bank in the quantitative analysis of economic policy questions (Meeraus (1983), Brooke, Kendrick and Meeraus (1987)). At the time of its conception and initial development, linear programming (LP) was the standard framework in which market equilibrium models were con...

The Path Solver: A Non-Monotone Stabilization Scheme for Mixed Complementarity Problems

The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a path-generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length acceptance criterion and a non-monotone pathsearch are then used to choose the next iterate. The algorith...

QPCOMP: A quadratic programming based solver for mixed complementarity problems

QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriell14], this algorithm represents a signiicant advance in robustness at no cost in eeciency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously diierentiable, pseudo-...

Infeasible path following algorithms for linear complementarity problems