A non-interior-point smoothing method for variational inequality problem

Authors:
Xiangsong Zhang;Sanyang Liu;Zhenhua Liu
Affiliations:
Applied Mathematics Department, Xidian University, Xi'an, Shaanxi 710071, PR China;Applied Mathematics Department, Xidian University, Xi'an, Shaanxi 710071, PR China;Applied Mathematics Department, Xidian University, Xi'an, Shaanxi 710071, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, we focus on the variational inequality problem. Based on the Fischer-Burmeister function with smoothing parameters, the variational inequality problem can be reformulated as a system of parameterized smooth equations, a non-interior-point smoothing method is presented for solving the problem. The proposed algorithm not only has no restriction on the initial point, but also has global convergence and local quadratic convergence, moreover, the local quadratic convergence is established without a strict complementarity condition. Preliminary numerical results show that the algorithm is promising.