A pathsearch damped Newton method for computing general equilibria.

*(English)*Zbl 0868.90012Summary: Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearch damped Newton method for solving such problems. Our algorithm improves on the typical Newton method (which generates and solves a sequence of LCPs) in both speed and robustness. The underlying complementarily problem is reformulated as a normal map so that standard algorithmic enhancements of Newton’s method for solving nonlinear equations can be easily applied. The solver is implemented as a GAMS subsystem, using an interface library developed for this purpose. Computational results obtained from a number of test problems arising in economics are given.

##### MSC:

91B50 | General equilibrium theory |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

##### Keywords:

computable general equilibrium models; variational inequalities; pathsearch damped Newton method
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\textit{S. P. Dirkse} and \textit{M. C. Ferris}, Ann. Oper. Res. 68, 211--232 (1996; Zbl 0868.90012)

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