MILES: A Mixed Inequality and nonLinear Equation Solver

MILES is a solver for nonlinear complementarity problems and nonlinear systems of equations. This solver can be accessed indirectly through GAMS/MPSGE or GAMS/MCP. This paper documents the solution algorithm, user options, and program output. The purpose of the paper is to provide users of GAMS/MPSGE and GAMS/MCP an overview of how the MCP solver works so that they can use the program effectively.

[1]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[2]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[3]  S. M. Robinson,et al.  A quadratically-convergent algorithm for general nonlinear programming problems , 1972, Math. Program..

[4]  William W. Hogan,et al.  Energy policy models for project independence , 1975, Comput. Oper. Res..

[5]  Ikuyo Kaneko,et al.  A linear complementarity problem with an n by 2n “P”-matrix , 1978 .

[6]  B. Eaves.  A Locally Quadratically Convergent Algorithm for Computing Stationary Points. , 1978 .

[7]  N. Josephy.  Newton's Method for Generalized Equations. , 1979 .

[8]  W. Rheinboldt,et al.  Pathways to Solutions, Fixed Points, and Equilibria. , 1983 .

[9]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[10]  L. Mathiesen.  Computation of economic equilibria by a sequence of linear complementarity problems , 1985 .

[11]  William H. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[12]  P. Gill,et al.  Maintaining LU factors of a general sparse matrix , 1987 .

[13]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[14]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[15]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[16]  Jon Lee,et al.  Crashing a maximum-weight complementary basis , 1992, Math. Program..

[17]  S. Dirkse.  Robust solution of mixed complementary problems , 1994 .