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An operator splitting method for monotone variational inequalities with a new perturbation strategy

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Abstract

In variational inequalities arising from applications such as engineering, economics and transportation, partial mappings are usually unknown, e.g., the demand function in traffic assignment problem. As a consequence, classical methods can not deal with this class of problems. On the other hand, the recently developed methods require restrictive conditions such as strong monotonicity of some mappings, which excludes many interesting applications. In this paper, we propose an operator splitting method with a new perturbation strategy for solving variational inequality problems with partially unknown mappings. Under the mild condition that the underlying mapping is monotone, we prove the global convergence of the method. We also report some preliminary numerical results which show that the new algorithm is also interesting from the numerical point of view.

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Acknowledgements

We are grateful to the anonymous referee for the helpful comments and suggestions, which help us improve the paper greatly.

Author information

Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Zhili Ge & Qin Ni

  2. Basic Sciences Department, Nanjing Polytechnic Institute, Nanjing, 210048, China

    Zhili Ge

  3. Key Laboratory for NSLSCS of Jiangsu Province, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Deren Han

  4. School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    David Z. W. Wang

Authors
  1. Zhili Ge
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  2. Deren Han
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  3. Qin Ni
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  4. David Z. W. Wang
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Corresponding author

Correspondence to Qin Ni.

Additional information

Z. Ge is supported by Funding of Jiangsu Innovation Program for Graduate Education (KYZZ15_0087) and the Fundamental Research Funds for the Central Universities. D. Han is supported by NSFC (11371197; 11431002; 11625005). Q. Ni is supported by NSFC (11471159; 11571169, 61661136001, 11611130018), and the Natural Science Foundation of Jiangsu Province (BK20141409).

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Ge, Z., Han, D., Ni, Q. et al. An operator splitting method for monotone variational inequalities with a new perturbation strategy. Optim Lett 12, 103–122 (2018). https://doi.org/10.1007/s11590-016-1103-8

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  • DOI: https://doi.org/10.1007/s11590-016-1103-8

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