MILES

MILES is a solver for nonlinear complementarity problems and nonlinear systems of equations. The solver can be accessed through GAMS to solve MPSGE or MCP models. This paper documents the solution algorithm, user options, and solver output. The purpose of the paper is to provide users of MILES an overview of how the solver works so that they can use it effectively. MILES is a Fortran-based solver for nonlinear complementarity problems and nonlinear systems of equations. The solution procedure is a generalized Newton method with a backtracking line search. This code is based on an algorithm investigated by Mathiesen (1985) who proposed a modeling format and sequential method for solving economic equilibrium models. The method is closely related to algorithms proposed by Robinson (1975), Hogan (1977), Eaves (1978) and Josephy (1979). In this implementation, subproblems are solved as linear complementarity problems (LCPs), using an extension of Lemke’s almost-complementary pivoting scheme in which upper and lower bounds are represented implicitly. The linear solver employs the basis factorization package LUSOL, developed by Gill et al. (1991).