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Extension of GAMS for complementarity problems arising in applied economic analysis. (English) Zbl 0877.90074
Summary: This paper introduces new features of the GAMS modeling language which have been developed for solving nonlinear complementarity problems. The paper defines the ‘mixed complementarity problem’ (MCP) and its various manifestations. Complementarity formulations for three economic models are developed, and computational benchmarks are presented for two large-scale MCP solvers. Finally, procedures for local sensitivity analysis are described.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91B99 Mathematical economics
90C31 Sensitivity, stability, parametric optimization
90C06 Large-scale problems in mathematical programming
Software:
GAMS; MILES; PATH Solver
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References:
[1] Adelman, I.; Robinson, S., Income distribution policy in developing countries: A case study of Korea, (1978), Oxford University Press London
[2] Anstreicher, K.; Lee, J.; Rutherford, T.F., Crashing a maximum weight complementary basis, Mathematical programming, 54, 281-290, (1992) · Zbl 0764.90082
[3] Brooke, T.; Kendrick, D.; Meeraus, A., ()
[4] Defermos, S., An iterative scheme for variational inequalities, Mathematical programming, 26, 40-47, (1982)
[5] Dantzig, G., Linear programming and extensions, (1963), Princeton University Press Princeton, NJ · Zbl 0108.33103
[6] Dirkse, S.; Ferris, M., The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems, (), Sept.
[7] Duffie, D.; Shafer, W., Equilibrium in incomplete markets: I. A basic model of generic existence, Journal of mathematical economics, 14, 285-300, (1985) · Zbl 0604.90029
[8] Eaves, B.C., A locally quadratically convergent algorithm for computing stationary points, () · Zbl 0441.65039
[9] Gale, D., The theory of linear economic models, (1960), University of Chicago Press Chicago, IL · Zbl 0114.12203
[10] Gill, P.; Murray, W.; Saunders, M.A.; Wright, M.H., Maintaining LU factors of a general sparse matrix, Linear algebra and its applications, 88/89, 239-270, (1991) · Zbl 0618.65019
[11] Goreux, L.M.; Manne, A.S., Multi-level planning: case studies in Mexico, (1973), North-Holland Amsterdam
[12] Harker, P., Alternative models of spatial competition, Operations research, 34, 410-425, (1986) · Zbl 0602.90018
[13] Harker, P.; Pang, J.S., Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical programming, B 38, 161-190, (1990) · Zbl 0734.90098
[14] Hogan, W.W., Energy policy models for project independence, Computation and operations research, 2, 251-271, (1975)
[15] Josephy, N.H., Newton’s method for generalized equations, ()
[16] Kojima, M.; Megiddo, N.; Noma, T.; Yoshise, A., A unified approach to interior point algorithms for linear complementarity problems, () · Zbl 0745.90069
[17] Laan, G.van der; Talman, A.J.J., An algorithm for the linear complementarity problem with upper and lower bounds, Journal of optimization theory and applications, 62, 151-163, (1985) · Zbl 0651.90086
[18] Laan, G.van der; Talman, A.J.J.; van der Heyden, L., Simplicial variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using a general labelling, Mathematics of operations research, 12, 337-397, (1987) · Zbl 0638.90096
[19] Lemke, C.E.; Howson, J.T., Equilibrium points of bimatrix games, SIAM review, 12, 413-423, (1964) · Zbl 0128.14804
[20] Mathiesen, L., Computation of economic equilibrium by a sequence of linear-complementarity problems, () · Zbl 0579.90093
[21] Meeraus, A., An algebraic approach to modeling, Journal of economic dynamics and control, 5, (1983)
[22] Ralph, D., Global convergence of damped Newton’s method for nonsmooth equations, via the path search, Mathematics of operations research, 19, 352-371, (1994) · Zbl 0819.90102
[23] Robinson, S., A quadratically-convergent algorithm for general nonlinear programming problems, Mathematical programming study, 3, 145-156, (1972) · Zbl 0264.90041
[24] Rutherford, T., Applied general equilibrium modeling, ()
[25] Rutherford, T., Sequential joint maximization, ()
[26] Rutherford, T., Applied general equilibrium modeling using MPS/GE as a GAMS subsystem, ()
[27] Rutherford, T., MILES: A mixed inequality and nonlinear equation solver, ()
[28] Samuelson, P., Spatial price equilibrium and linear programming, American economic review, 42, 283-303, (1952)
[29] Takayama, T.; Judge, G.G., Spatial and temporal price and allocation models, (1971), North-Holland Amsterdam
[30] Varian, H., Microeconomic analysis, (1992), Norton New York, NY
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