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Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems

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  • J. H. Wu

    (Université de Montréal)

Abstract

In this paper, we present a long-step primal path-following algorithm and prove its global convergence under usual assumptions. It is seen that the short-step algorithm is a special case of the long-step algorithm for a specific selection of the parameters and the initial solution. Our theoretical result indicates that the long-step algorithm is more flexible. Numerical results indicate that the long-step algorithm converges faster than the short-step algorithm.

Suggested Citation

  • J. H. Wu, 1998. "Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 509-531, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021786630040
    DOI: 10.1023/A:1021786630040
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    References listed on IDEAS

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    1. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    2. Jong-Shi Pang, 1990. "Newton's Method for B-Differentiable Equations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 311-341, May.
    3. 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.
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    Cited by:

    1. T. T. Hue & J. J. Strodiot & V. H. Nguyen, 2004. "Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 119-145, April.
    2. 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.

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