On finite convergence of proximal point algorithms for variational inequalities |
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Authors: | Naihua Xiu Jianzhong Zhang |
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Institution: | a Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, China b Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong |
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Abstract: | In this paper, we first characterize finite convergence of an arbitrary iterative algorithm for solving the variational inequality problem (VIP), where the finite convergence means that the algorithm can find an exact solution of the problem in a finite number of iterations. By using this result, we obtain that the well-known proximal point algorithm possesses finite convergence if the solution set of VIP is weakly sharp. As an extension, we show finite convergence of the inertial proximal method for solving the general variational inequality problem under the condition of weak g-sharpness. |
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Keywords: | Variational inequalities Proximal point algorithm Inertial proximal method Finite convergence Weak sharpness |
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