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Modified Primal Path-Following Scheme for the Monotone Variational Inequality Problem

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  • J. H. Wu

    (Université de Montréal)

Abstract

Recently, several interior-point methods have been developed under a scaled Lipschitz condition which may be strong in general. In this paper, we develop a modified path-following scheme which does not require the above condition. Its global convergence is proved under only the assumptions of monotonicity and differentiability of the mapping. The scheme is adapted to the network equilibrium problem (a nonlinear multicommodity network flow problem) with a simplicial decomposition technique.

Suggested Citation

  • J. H. Wu, 1997. "Modified Primal Path-Following Scheme for the Monotone Variational Inequality Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 189-208, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022643630525
    DOI: 10.1023/A:1022643630525
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    1. K. O. Kortanek & Jishan Zhu, 1993. "A Polynomial Barrier Algorithm for Linearly Constrained Convex Programming Problems," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 116-127, February.
    2. Mustafa C. Pinar & Stavros A. Zenios, 1992. "Parallel Decomposition of Multicommodity Network Flows Using a Linear-Quadratic Penalty Algorithm," INFORMS Journal on Computing, INFORMS, vol. 4(3), pages 235-249, August.
    3. Lawphongpanich, Siriphong & Hearn, Donald W., 1984. "Simplical decomposition of the asymmetric traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 123-133, April.
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    Cited by:

    1. G. Salmon & V. H. Nguyen & J. J. Strodiot, 2000. "Coupling the Auxiliary Problem Principle and Epiconvergence Theory to Solve General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 629-657, March.
    2. Wong, K.I. & Wong, S.C. & Yang, Hai & Wu, J.H., 2008. "Modeling urban taxi services with multiple user classes and vehicle modes," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 985-1007, December.
    3. Y. B. Zhao & J. Y. Han, 1999. "Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 659-679, September.

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