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Global Exponential Stability of a Neural Network for Inverse Variational Inequalities

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  • Phan Tu Vuong

    (University of Southampton)

  • Xiaozheng He

    (Rensselaer Polytechnic Institute)

  • Duong Viet Thong

    (National Economics University)

Abstract

We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions, we establish the exponential stability of the proposed neural network. A discrete version of the proposed neural network is considered, leading to a new projection method for solving inverse variational inequalities, for which we obtain the linear convergence. We illustrate the effectiveness of the proposed neural network and its explicit discretization by considering applications in the road pricing problem arising in transportation science. The results obtained in this paper provide a positive answer to a recent open question and improve several recent results in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01915-x
    DOI: 10.1007/s10957-021-01915-x
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    References listed on IDEAS

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    1. 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.
    2. Jiang, Yaning & Cai, Xingju & Han, Deren, 2020. "Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities," European Journal of Operational Research, Elsevier, vol. 280(2), pages 417-427.
    3. M. Pappalardo & M. Passacantando, 2002. "Stability for Equilibrium Problems: From Variational Inequalities to Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 567-582, June.
    4. 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.
    5. 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.
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