Abstract
This paper presents the results of extensive computational testing of the modified damped Newton algorithm for solving variational inequality problems presented in Part I [8].
Similar content being viewed by others
References
D.P. Bertsekas and E.M. Gafni, “Projection methods for variational inequalities with application to the traffic assignment problem,”Mathematical Programming Study 17 (1982) 139–159.
P.T. Harker, “Alternative models of spatial competition,”Operations Research 34 (1986) 410–425.
P.T. Harker, “Accelerating the convergence of the diagonalization and projection algorithms for finitedimensional variational inequalities,”Mathematical Programming 41 (1988) 29–59.
P.T. Harker, “Dispersed spatial price equilibrium,”Environment and Planning A 20 (1988) 353–368.
P.T. Harker and J.S. Pang, “A damped-Newton method for the linear complementarity problem,” in: G. Allgower and K. Georg, ed.,AMS Transactions on Applied Mathematics 26 (1990) 265–284.
P.T. Harker and J.S. Pang, “Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications,”Mathematical Programming B 48 (1990) 1–60.
P.T. Harker and B. Xiao, “Newton's method for the nonlinear complementarity problem: a B-differentiable equation approach,”Mathematical Programming 48 (1990) 339–357.
B. Xiao and P.T. Harker, “A nonsmooth Newton method for variational inequalities, I: theory,”Mathematical Programming 65 (1994) 151–194.
D.M. Himmelblau,Applied Nonlinear Programming (McGraw-Hill, Inc., 1972).
N.H. Josephy, “Newton's method for generalized equations,” Technical Report No. 1965, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979).
J. MacKinnon, “A technique for the solution of spatial equilibrium models,”Journal of Regional Science 16 (1976) 293–307.
L. Mathiesen, “Computation of economic equilibria by a sequence of linear complementarity problems,”Mathematical Programming Study 23 (1985) 144–162.
L. Mathiesen, “Computational experience in solving equilibrium models by a sequence of linear complementarity problems,”Operations Research 33 (1985) 1225–1250.
K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Helderman-Verlag, Berlin, 1988).
M.J.D. Powell, “A method for nonlinear constraints in minimization problems,” in: R. Fletcher, ed.,Optimization (Academic Press, New York, 1969).
J. Rowse, “On the solution of spatial equilibrium models,”Decision Sciences 13 (1982) 619–637.
T. Rutherford, “Applied general equilibrium modeling,” Ph.D. dissertation, Department of Operations Research, Stanford University (Stanford, CA, 1986).
H.E. Scarf and T. Hansen,Computation of Economic Equilibria (Yale University Press, New Haven, Connecticut, 1973).
R.L. Tobin, “A variable dimension solution approach for the general spatial price equilibrium problem,”Mathematical Programming 40 (1988) 33–51.
Author information
Authors and Affiliations
Additional information
Corresponding author.
Rights and permissions
About this article
Cite this article
Xiao, B., Harker, P.T. A nonsmooth Newton method for variational inequalities, II: Numerical results. Mathematical Programming 65, 195–216 (1994). https://doi.org/10.1007/BF01581696
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01581696