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An inexact logarithmic-quadratic proximal augmented Lagrangian method for a class of constrained variational inequalities

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  • M. Li
  • H. Shao
  • B. He

Abstract

The augmented Lagrangian method is attractive in constraint optimizations. When it is applied to a class of constrained variational inequalities, the sub-problem in each iteration is a nonlinear complementarity problem (NCP). By introducing a logarithmic-quadratic proximal term, the sub-NCP becomes a system of nonlinear equations, which we call the LQP system. Solving a system of nonlinear equations is easier than the related NCP, because the solution of the NCP has combinatorial properties. In this paper, we present an inexact logarithmic-quadratic proximal augmented Lagrangian method for a class of constrained variational inequalities, in which the LQP system is solved approximately under a rather relaxed inexactness criterion. The generated sequence is Fejér monotone and the global convergence is proved. Finally, some numerical test results for traffic equilibrium problems are presented to demonstrate the efficiency of the method. Copyright Springer-Verlag 2007

Suggested Citation

  • M. Li & H. Shao & B. He, 2007. "An inexact logarithmic-quadratic proximal augmented Lagrangian method for a class of constrained variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 183-201, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:183-201
    DOI: 10.1007/s00186-007-0145-1
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    References listed on IDEAS

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    1. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
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    Cited by:

    1. Yuxiang Yang & Zuqing Huang & Qiang Patrick Qiang & Gengui Zhou, 2017. "A Mathematical Programming Model with Equilibrium Constraints for Competitive Closed-Loop Supply Chain Network Design," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-31, October.

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