Unconstrained Optimization Reformulations of Variational Inequality Problems |
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| Authors: | N. Yamashita K. Taji M. Fukushima |
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| Affiliation: | (1) Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, Kyoto, Japan;(2) Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara, Japan;(3) Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, Kyoto, Japan |
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| Abstract: | ![]()
Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the D-gap function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap function. |
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| Keywords: | Variational inequality problems unconstrained optimization reformulations global error bounds descent methods |
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