Convergence Properties of Projection and Contraction Methods for Variational Inequality Problems |
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Authors: | N Xiu C Wang J Zhang |
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Affiliation: | (1) Department of Applied Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China nhxiu@center.njtu.edu.cn , CN;(2) Institute of Operations Research, Qufu Normal University, Qufu 273165, People's Republic of China , CN;(3) Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong mazhang@cityu.edu.hk , HK |
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Abstract: | In this paper we develop the convergence theory of a general class of projection and contraction algorithms (PC method),
where an extended stepsize rule is used, for solving variational inequality (VI) problems. It is shown that, by defining a
scaled projection residue, the PC method forces the sequence of the residues to zero. It is also shown that, by defining a
projected function, the PC method forces the sequence of projected functions to zero. A consequence of this result is that
if the PC method converges to a nondegenerate solution of the VI problem, then after a finite number of iterations, the optimal
face is identified. Finally, we study local convergence behavior of the extragradient algorithm for solving the KKT system
of the inequality constrained VI problem. \keywords{Variational inequality, Projection and contraction method, Predictor-corrector
stepsize, Convergence property.} \amsclass{90C30, 90C33, 65K05.}
Accepted 5 September 2000. Online publication 16 January 2001. |
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Keywords: | , Variational inequality, Projection and contraction method, Predictor-corrector stepsize, Convergence property,,,,,,AMS Classification, 90C30, 90C33, 65K05, |
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