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- Title
A globally and superlinearly convergent quasi-Newton method for general box constrained variational inequalities without smoothing approximation.
- Authors
Xuebin Wang; Changfeng Ma; Meiyan Li
- Abstract
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.
- Subjects
NEWTON-Raphson method; VARIATIONAL inequalities (Mathematics); APPROXIMATION algorithms; DIFFERENTIAL inequalities; ALGORITHMS
- Publication
Journal of Global Optimization, 2011, Vol 50, Issue 4, p675
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-010-9629-2