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Complementarity Problem Net: Algorithms and Applications; Complementarity Problem NET;As a result of more than three decades of research, the subject of;complementarity problems, with its diverse applications in engineering,;economics, and sciences, has become a well-established and fruitful;discipline within mathematical programming. Several monographs;and surveys have documented the basic theory, algorithms, and applications;of complementarity problems and their role in optimization theory.;This page serves as a center for information regarding research in;complementarity problems. As such there is a listing of meetings;of interest to the community, some pointers to software for;complementarity problems as well as links to other pages of interest.;A listing of researchers and some application areas are also given.; Table of Contents;; Directory of Researchers in Complementarity;; Software for Complementarity Problems;; Applications of Complementarity;; Relevant Web Links;;Directory of Complementarity Researchers;Software for Complementarity Problems;MCPLIB:;A collection of nonlinear mixed complementarity problems, problem;description, and how to access the GAMS source files for;these problems.;Complementarity Toolbox for MATLAB:;This (evolving) freely available toolbox consists of several mex and;m-files. These allow all the MCPLIB problems to be accessed from;MATLAB without access to GAMS. The mex files give function;evaluations and sparse Jacobian evaluations. Machine specific;versions can be downloaded.;The PATH solver is also available in this toolbox, more details below.;Solver Interface to GAMS:;This describes a library of routines that are;available to help hook your solver to the GAMS/MCP modeling language.;Contact steve@gams.com, rutherford@colorado.edu or ferris@cs.wisc.edu;for further details.;MILES:;MILES is an extension of the classical;Josephy-Newton method for NCP in which the solution to each linearized;subproblem is computed via Lemke's almost-complementary pivot algorithm.;This Newton point is used to define;the Newton direction, which is then used in a damped;linesearch. The merit function used measures both the violation in;feasibility and in complementarity. MILES also employs a restart;procedure in cases where the Newton point cannot be computed due to;termination in a secondary ray.;Every linearized subproblem is rescaled to equilibrate the elements;appearing in the data of the subproblem.;PATH:;(Runs under GAMS/MCP;or directly under MATLAB):;The PATH solver applies techniques similar;to those used in Newton methods for smooth systems to a;nonsmooth reformulation of the MCP. The algorithm;consists of a sequence of major iterations, each consisting of an;approximation or linearization step similar to that of MILES,;the construction of a path;to the Newton point (the solution to the approximation), and a;possible search of this path. When the Newton point does not exists or the;path cannot be entirely constructed, a step along the partially;computed path is taken before the problem is relinearized. A;nonmonotone watchdog strategy is employed in applying the path search;;this helps avoid convergence to local minima of the norm function for;the underlying nonsmooth equation and keeps the number of function;evaluations required as small as possible. A list of solver options;is given in the document;;NE/SQP: The NE/SQP algorithm is based upon;reformulating the NCP as a system of nonsmooth equations.;The NE/SQP algorithm implemented as a GAMS/MCP solver, its robustness;improved using a proximal perturbation strategy giving the;QPCOMP algorithm.;The nonsmoothness of the equations is;handled using directional derivatives of H.;SMOOTH;;The SMOOTH algorithm is based upon;reformulating the NCP as a system of nonsmooth equations and then;approximately solving a sequence of smooth approximations, which lead;to a zero of the nonsmooth system.;At each iteration,;a smooth approximation to the original system is formed where the;accuracy of the approximation is determined by the residual of the;current point. This is implemented as a GAMS/MCP system.;Other solvers;have been implemented as subsystems of GAMS and are compared in this paper.;Applications of Complementarity; Engineering;and Economic Applications of Complementarity Problems.;This paper lists many of the known applications of complementarity problems.; MPSGE: A preprocessor for the GAMS modeling language that;allows economic equilibrium problems to be formulated easily. See the;GAMS home page for further information.; NEMS;The National Energy Modeling System. There are several papers on related;algorithms;and a paper giving an;overview of the project.;; Relevant Web Links; Look up Michael Trick's Operations Research Page for some interesting OR links.; Look up Interior-Point Web for information on interior point;methods at the Argonne National Laboratories archive.;;Last modified: October 24, 1996 by Michael C. Ferris;ferris@cs.wisc.edu;