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Finite convergence of a projected proximal point algorithm for the generalized variational inequalities. (English) Zbl 1247.90264
Summary: In this work, we mainly establish the finite convergence of the projected proximal point algorithm for generalized variational inequalities under a weak sharp condition, which extends the corresponding result for the classical variational inequalities.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C51 Interior-point methods
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[1] Burke, J.V.; Ferris, M.C., Weak sharp minima in mathematical programming, SIAM J. control optim., 31, 1340-1359, (1993) · Zbl 0791.90040
[2] Facchinei, F.; Pang, J.S., Finite-dimensional variational inequalities and complementarity problems, (2003), Springer New York · Zbl 1062.90002
[3] Farouq, N., Pseudomonotone variational inequalities: convergence of proximal methods, J. optim. theory appl., 109, 311-326, (2001) · Zbl 0993.49006
[4] Iusem, A.N., A generalized proximal point algorithm for the variational inequality problem in Hilbert space, SIAM J. optim., 8, 197-216, (1998) · Zbl 0911.90273
[5] Kiwiel, K.C., Proximal minimization methods with generalized Bergman function, SIAM J. control optim., 35, 1142-1168, (1997) · Zbl 0890.65061
[6] Konnov, I.V., Application of the proximal point method to nonmonotone equilibrium problems, J. optim. theory appl., 119, 317-333, (2003) · Zbl 1084.49009
[7] Luque, F.J., Asymptotic convergence analysis of the proximal point algorithm, SIAM J. control optim., 22, 277-293, (1984) · Zbl 0533.49028
[8] Marcotte, P.; Zhu, D., A cutting plane for quasimonotone variational inequalities, Comput. optim. appl., 20, 317-324, (2001) · Zbl 1054.90073
[9] Martinet, B., Régularisation d’inéquations variationelles par approximations successives, Rev. fr. inform. rech. oper., 4, 154-158, (1970) · Zbl 0215.21103
[10] Moreau, J.J., Decomposition orthogonale d’un espace hilbertien selon deux cones mutuellement polaires, C. R. acad. sci., 255, 238-240, (1962) · Zbl 0109.08105
[11] Noor, M.A., Some developments in general variational inequalities, Appl. math. comput., 152, 199-277, (2004) · Zbl 1134.49304
[12] Polyak, B.T., Introduction to optimization, (1987), Optimization Software Inc., Publications Division New York · Zbl 0652.49002
[13] Rockafellar, R.T., Monotone operators and the proximal point algorithm, SIAM J. control optim., 14, 877-898, (1976) · Zbl 0358.90053
[14] Xia, F.Q.; Huang, N.J., A projection – proximal point algorithm for solving generalized variational inequalities, J. optim. theory appl., 150, 98-117, (2011) · Zbl 1242.90267
[15] Xiu, N.H.; Zhang, J.Z., On finite convergence of proximal point algorithms for variational inequalities, J. math. anal. appl., 312, 148-158, (2005) · Zbl 1083.49011
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