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Inverse variational inequalities with projection-based solution methods

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  • He, Xiaozheng
  • Liu, Henry X.

Abstract

An inverse variational inequality is defined as to find a vector , such thatIf an inverse function u = F-1(x) exists, the above inverse variational inequality could be transformed as a regular variational inequality. However, in reality, it is not uncommon that the inverse function of F-1(x) does not have explicit form, although its functional values can be observed. Existing line search algorithms cannot be applied directly to solve such inverse variational inequalities. In this paper, we propose two projection-based methods using the co-coercivity of mapping F. A self-adaptive strategy is developed to determine the step sizes efficiently when the co-coercivity modulus is unknown. The convergence of the proposed methods is proved rigorously.

Suggested Citation

  • He, Xiaozheng & Liu, Henry X., 2011. "Inverse variational inequalities with projection-based solution methods," European Journal of Operational Research, Elsevier, vol. 208(1), pages 12-18, January.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:1:p:12-18
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    References listed on IDEAS

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    1. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X., 2010. "Solving a class of constrained 'black-box' inverse variational inequalities," European Journal of Operational Research, Elsevier, vol. 204(3), pages 391-401, August.
    2. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X. & Wu, Ting, 2009. "Self-adaptive projection method for co-coercive variational inequalities," European Journal of Operational Research, Elsevier, vol. 196(1), pages 43-48, July.
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    Cited by:

    1. Phan Tu Vuong & Xiaozheng He & Duong Viet Thong, 2021. "Global Exponential Stability of a Neural Network for Inverse Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 915-930, September.

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