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Projected subgradient techniques and viscosity methods for optimization with variational inequality constraints

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  • Maingé, Paul-Emile

Abstract

In this paper, we propose an easily implementable algorithm in Hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities. The proposed method combines two strategies: projected subgradient techniques and viscosity-type approximations. The involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints.

Suggested Citation

  • Maingé, Paul-Emile, 2010. "Projected subgradient techniques and viscosity methods for optimization with variational inequality constraints," European Journal of Operational Research, Elsevier, vol. 205(3), pages 501-506, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:3:p:501-506
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    References listed on IDEAS

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    1. M. A. Noor, 2004. "Auxiliary Principle Technique for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 371-386, August.
    2. T. T. Hue & J. J. Strodiot & V. H. Nguyen, 2004. "Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 119-145, April.
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    Cited by:

    1. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.

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