Find out how to access previewonly content
Accelerating the convergence of the diagonalization and projection algorithms for finitedimensional variational inequalities
 Patrick T. Harker
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This paper presents an acceleration step for the linearly convergent diagonalization and projection algorithms for finitedimensional variational inequalities which is reminiscent of a PARTAN step in nonlinear programming. After establishing the convergence of this technique for both algorithms, several numerical examples are presented to illustrate the sometimes dramatic savings in computation time which this simple acceleration step yields.
 B.H. Ahn,Computation of Market Equilibria for Policy Analysis: The Project Independence Evaluation Study (PIES) (Garland, New York, NY, 1979).
 D.P. Bertsekas and E.M. Gafni, “Projection methods for variational inequalities with application to the traffic assignment problem,”Mathematical Programming Study 16 (1982) 139–159.
 J. Bisschop and A. Meeraus, “On the development of general algebraic modeling systems in a strategic planning environment,”Mathematical Programming Study 20 (1982) 1–29.
 S. Dafermos, “Traffic equilibrium and variational inequalities,”Transportation Science 14 (1980) 42–54.
 S. Dafermos, “An iterative method for variational inequalities,”Mathematical Programming 26 (1983) 40–47.
 T.L. Friesz, R.L. Tobin and P.T. Harker, “Variational inequalities and convergence of diagonalization methods for derived demand network equilibrium problems,” Working Paper CUEFNEM1981–101, Department of Civil Engineering, University of Pennsylvania, 1981.
 T.L. Friesz, R.L. Tobin, T.E. Smith and P.T. Harker, “A nonlinear complementarity formulation and solution procedure for the general derived demand network equilibrium problem,”Journal of Regional Science 23 (1983) 337–359.
 D. Gabay and H. Moulin, “On the uniqueness and stability of Nashequilibria in noncooperative games,” in: A. Bensoussan, P. Kleindorfer and C.S. Taperio, eds.,Applied Stochastic Control in Econometrics and Management Science (NorthHolland, Amsterdam, 1980).
 R. Glowinski, J.L. Lions and R. Tremolieres,Analyse Numerique des Inequations Variationelles, Methodes Mathematiques de l'Informatique (Bordas, Paris, 1976).
 J.H. Hammond, “Solving asymmetric variational inequality problems and systems of equations with generalized nonlinear programming,” Ph.D. dissertation, Department of Mathematics, MIT, Cambridge, MA, 1984.
 J.H. Hammond and T.L. Magnanti, “Generalized descent methods for asymmetric systems of equations and variational inequalities,” Working Paper OR 13785, Operations Research Center, M.I.T., Cambridge, MA, 1985.
 P.T. Harker, “A variational inequality approach for the determination of oligopolistic market equilibrium,”Mathematical Programming 30 (1984) 105–111.
 P.T. Harker, “Alternative models of spatial competition,”Operations Research 34 (1986) 410–425.
 P.T. Harker and T.L. Friesz, “Prediction of intercity freight flows, I: theory and II: mathematical formulations,”Transportation Research 20B (1986) 139–153 and 155–174.
 F.H. Murphy, H.D. Sherali and A.L. Soyster, “A mathematical programming approach for determining oligopolistic market equilibrium,”Mathematical Programming 24 (1982) 92–106.
 J.M. Ortega and W.C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).
 J.S. Pang, “Solution of the general multicommodity spatial equilibrium problem by variational and complementarity problems,”Journal of Regional Science 24 (1984) 403–414.
 J.S. Pang and D. Chan, “Iterative methods for variational and complementarity problems,”Mathematical Programming 24 (1982) 284–313.
 Title
 Accelerating the convergence of the diagonalization and projection algorithms for finitedimensional variational inequalities
 Journal

Mathematical Programming
Volume 41, Issue 13 , pp 2959
 Cover Date
 19880501
 DOI
 10.1007/BF01580752
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Variational inequalities
 iterative methods
 complementarity problems
 Nash equilibria
 traffic equilibria
 spatial price equilibria
 Industry Sectors
 Authors

 Patrick T. Harker ^{(1)}
 Author Affiliations

 1. Department of Decision Sciences, The Wharton School, University of Pennsylvania, 191046366, Philadelphia, PA, USA