A globally and superlinearly convergent quasi-Newton method for general box constrained variational inequalities without smoothing approximation

Authors:
Xuebin Wang;Changfeng Ma;Meiyan Li
Affiliations:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China 350007 and School of Mathematics & Computer Science, Guilin University of Electronic Technology, Guilin, China 5 ...;School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China 350007 and School of Mathematics & Computer Science, Guilin University of Electronic Technology, Guilin, China 5 ...;School of Mathematics & Computer Science, Guilin University of Electronic Technology, Guilin, China 541004
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

A new quasi-Newton algorithm for the solution of general box constrained variational inequality problem (GVI(l, u, F, f)) is proposed in this paper. It is based on a reformulation of the variational inequality problem as a nonsmooth system of equations by using the median operator. Without smoothing approximation, the proposed quasi-Newton algorithm is directly applied to solve this class of nonsmooth equations. Under appropriate assumptions, it is proved that the algorithmic sequence globally and superlinearly converges to a solution of the equation reformulation and also of GVI(l, u, F, f). Numerical results show that our new algorithm works quite well.