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Hybrid Steepest Descent Methods for Zeros of Nonlinear Operators with Applications to Variational Inequalities

Author

Listed:
  • L. C. Zeng

    (Shanghai Normal University)

  • S. Schaible

    (Chung Yuan Christian University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, the hybrid steepest descent methods are extended to develop new iterative schemes for finding the zeros of bounded, demicontinuous and φ-strongly accretive mappings in uniformly smooth Banach spaces. Two iterative schemes are proposed. Strong convergence results are established and applications to variational inequalities are given.

Suggested Citation

  • L. C. Zeng & S. Schaible & J. C. Yao, 2009. "Hybrid Steepest Descent Methods for Zeros of Nonlinear Operators with Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 75-91, April.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9501-4
    DOI: 10.1007/s10957-008-9501-4
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    3. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
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