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Finite termination of a Newton-type algorithm based on a new class of smoothing functions for the affine variational inequality problem

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  • Zhao, Na

Abstract

In this paper, we propose a new class of smoothing functions. Some favorable properties of the functions are investigated. By using the proposed functions, the affine variational inequality problem (AVI) is reformulated as a system of parameterized smooth equations. A Newton method with a projection-type testing procedure is proposed to solve the equations. Under mild assumptions, we show that the algorithm may find a maximally complementary solution to the monotone AVI in a finite number of iterations. Preliminary numerical results indicate that the proposed smoothing functions are valuable.

Suggested Citation

  • Zhao, Na, 2015. "Finite termination of a Newton-type algorithm based on a new class of smoothing functions for the affine variational inequality problem," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 926-934.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:926-934
    DOI: 10.1016/j.amc.2015.08.045
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    References listed on IDEAS

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    1. James V. Burke & Song Xu, 1998. "The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 719-734, August.
    2. He, Bing-sheng & Yang, Hai & Zhang, Chen-song, 2004. "A modified augmented Lagrangian method for a class of monotone variational inequalities," European Journal of Operational Research, Elsevier, vol. 159(1), pages 35-51, November.
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