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Local Convergence Analysis of Projection-Type Algorithms: Unified Approach

Author

Listed:
  • N.H. Xiu

    (Northern Jiaotong University)

  • J.Z. Zhang

    (City University of Hong Kong)

Abstract

In this paper, we use a unified approach to analyze the local convergence behavior of a wide class of projection-type methods for solving variational inequality problems. Under certain conditions, it is shown that, in a finite number of iterations, either the sequence of iterates terminates at a solution of the concerned problem or all iterates enter and remain in the relative interior of the optimal face and, hence, the subproblem reduces to a simpler form.

Suggested Citation

  • N.H. Xiu & J.Z. Zhang, 2002. "Local Convergence Analysis of Projection-Type Algorithms: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 211-230, October.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:1:d:10.1023_a:1019637315803
    DOI: 10.1023/A:1019637315803
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    References listed on IDEAS

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    1. A. Schwartz & E. Polak, 1997. "Family of Projected Descent Methods for Optimization Problems with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 1-31, January.
    2. Roman Sznajder & M. Seetharama Gowda, 1998. "Nondegeneracy Concepts for Zeros of Piecewise Smooth Functions," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 221-238, February.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. J. Z. Zhang & H. H. Xiu, 2001. "Local Convergence Behavior of Some Projection-Type Methods for Affine Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 205-216, January.
    5. A. N. Iusem, 1998. "On Some Properties of Generalized Proximal Point Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 337-362, February.
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    Cited by:

    1. Shin-ya Matsushita & Li Xu, 2014. "On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 701-715, June.
    2. R. U. Verma, 2004. "Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 203-210, April.
    3. Changyu Wang & Qian Liu & Cheng Ma, 2013. "Smoothing SQP algorithm for semismooth equations with box constraints," Computational Optimization and Applications, Springer, vol. 55(2), pages 399-425, June.

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