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New smooth gap function for box constrained variational inequalities

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Abstract

A new smooth gap function for the box constrained variational inequality problem (VIP) is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

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Authors and Affiliations

  1. School of Mathematical Science, Dalian University of Technology, Dalian, 116023, Liaoning Province, P. R. China

    Li-li Zhang  (张丽丽)

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116023, Liaoning Province, P. R. China

    Xing-si Li  (李兴斯)

Authors
  1. Li-li Zhang  (张丽丽)
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  2. Xing-si Li  (李兴斯)
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Corresponding author

Correspondence to Xing-si Li  (李兴斯).

Additional information

Communicated by Geng-dong CHENG

Project supported by the National Natural Science Foundation of China (Nos. 10902077, 11172209, and 10572031)

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Zhang, Ll., Li, Xs. New smooth gap function for box constrained variational inequalities. Appl. Math. Mech.-Engl. Ed. 34, 15–26 (2013). https://doi.org/10.1007/s10483-013-1649-x

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  • DOI: https://doi.org/10.1007/s10483-013-1649-x

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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