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On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities

Author

Listed:
  • Caihua Chen

    (Nanjing University)

  • Xiaoling Fu

    (Southeast University)

  • Bingsheng He

    (South University of Science and Technology of China
    Nanjing University)

  • Xiaoming Yuan

    (Hong Kong Baptist University)

Abstract

Projection-type methods are important for solving monotone linear variational inequalities. In this paper, we analyze the iteration complexity of two projection methods and accordingly establish their worst-case sublinear convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses. Our analysis does not require any error bound condition or the boundedness of the feasible set, and it is scalable to other methods of the same kind.

Suggested Citation

  • Caihua Chen & Xiaoling Fu & Bingsheng He & Xiaoming Yuan, 2017. "On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 914-928, March.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1051-6
    DOI: 10.1007/s10957-016-1051-6
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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