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Pseudomonotone Variational Inequalities: Convergence of the Auxiliary Problem Method

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  • N. El Farouq

    (Université Blaise Pascal)

Abstract

This paper deals with the convergence of the algorithm built on the auxiliary problem principle for solving pseudomonotone (in the sense of Karamardian) variational inequalities.

Suggested Citation

  • N. El Farouq, 2001. "Pseudomonotone Variational Inequalities: Convergence of the Auxiliary Problem Method," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 305-322, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1012234817482
    DOI: 10.1023/A:1012234817482
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    References listed on IDEAS

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    1. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    2. N. El Farouq & G. Cohen, 1998. "Progressive Regularization of Variational Inequalities and Decomposition Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 407-433, May.
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    Citations

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    Cited by:

    1. M.A. Noor, 2002. "Proximal Methods for Mixed Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 447-452, November.
    2. N. El Farouq, 2004. "Convergent Algorithm Based on Progressive Regularization for Solving Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 455-485, March.
    3. M. A. Noor, 2004. "Auxiliary Principle Technique for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 371-386, August.
    4. I.V. Konnov, 2003. "Application of the Proximal Point Method to Nonmonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 317-333, November.
    5. M.A. Noor, 2002. "Proximal Methods for Mixed Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 453-459, November.
    6. Arnaldo S. Brito & J. X. Cruz Neto & Jurandir O. Lopes & P. Roberto Oliveira, 2012. "Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 217-234, July.
    7. Duong Viet Thong & Phan Tu Vuong & Pham Ky Anh & Le Dung Muu, 2022. "A New Projection-type Method with Nondecreasing Adaptive Step-sizes for Pseudo-monotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 22(4), pages 803-829, December.
    8. Pham Khanh & Phan Vuong, 2014. "Modified projection method for strongly pseudomonotone variational inequalities," Journal of Global Optimization, Springer, vol. 58(2), pages 341-350, February.
    9. Friesz, Terry L. & Han, Ke & Bagherzadeh, Amir, 2021. "Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 336-352.
    10. N. N. Tam & J. C. Yao & N. D. Yen, 2008. "Solution Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 253-273, August.

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