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Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities

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  • Jiang, Yaning
  • Cai, Xingju
  • Han, Deren

Abstract

Inverse variational inequalities have broad applications in various disciplines, and some of them have very appealing structures. There are several algorithms (e.g., proximal point algorithms and projection-type algorithms) for solving the inverse variational inequalities in general settings, while few of them have fully exploited the special structures. In this paper, we consider a class of inverse variational inequalities that has a separable structure and linear constraints, which has its root in spatial economic equilibrium problems. To design an efficient algorithm, we develop an alternating direction method of multipliers (ADMM) based method by utilizing the separable structure. Under some mild assumptions, we prove its global convergence. We propose an improved variant that makes the subproblems much easier and derive the convergence result under the same conditions. Finally, we present the preliminary numerical results to show the capability and efficiency of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:2:p:417-427
    DOI: 10.1016/j.ejor.2019.05.044
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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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