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Some developments in general variational inequalities. (English) Zbl 1134.49304
Summary: General variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection, Wiener-Hopf equations, updating the solution, auxiliary principle, inertial proximal, penalty function, dynamical system and well-posedness. We also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection-type algorithms. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, results presented here continue to hold for these problems. Several open problems have been suggested for further research in these areas.

MSC:
49J40Variational methods including variational inequalities
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
49Q12Sensitivity analysis
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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References:
[1] Al-Said, A. E.: A family of numerical methods for solving third-order boundary value problems. Inter. J. Math. 1, 367-375 (2002) · Zbl 0987.65071
[2] Al-Said, E. A.; Noor, M. Aslam: Cubic splines method for a system of third-order boundary value problems. Appl. math. Comput. 142, 195-204 (2003) · Zbl 1022.65082
[3] Al-Said, E. A.; Noor, M. Aslam; Khalifa, A. K.: Finite difference schemes for variational inequalities. J. optim. Theory appl. 89, 453-459 (1996) · Zbl 0848.49007
[4] Al-Said, E. A.; Noor, M. Aslam; Rassias, T. M.: Numerical solutions of third-order obstacle problems. Int. J. Comput. math. 69, 75-84 (1998) · Zbl 0905.65074
[5] Alvarez, F.: On the minimization property of a second order dissipative system in Hilbert space. SIAM J. Control optim. 38, 1102-1119 (2000) · Zbl 0954.34053
[6] Alvarez, F.; Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-valued anal. 9, 3-11 (2001) · Zbl 0991.65056
[7] Attouch, H.; Alvarez, F.: The heavy ball with friction dynamical system for convex constrained minimization problems. Lecture notes econ. Math. syst. 481, 25-35 (2000) · Zbl 0980.90062
[8] Baiocchi, C.; Capelo, A.: Variational and quasi-variational inequalities. (1984) · Zbl 0551.49007
[9] Bertsekas, D. P.; Tsitsiklis, J.: Parallel and distributed computation: numerical methods. (1989) · Zbl 0743.65107
[10] Blum, E.; Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. student 63, 325-333 (1994) · Zbl 0888.49007
[11] Brezis, H.: Operateurs maximaux monotones et semi-groups de contractions dans LES espaces de Hilbert. (1973)
[12] Burke, J. V.; More, J. J.: On the identification of active constraints. SIAM J. Num. anal. 25, 1197-1211 (1988) · Zbl 0662.65052
[13] Cohen, G.: Auxiliary problem principle extended to variational inequatlities. J. optim. Theory appl. 59, 325-333 (1988) · Zbl 0628.90066
[14] Cottle, R. W.: Nonlinear programs with positively bounded Jacobians. SIAM J. Appl. math. 14, 147-158 (1966) · Zbl 0158.18903
[15] Cottle, R. W.; Pang, J. S.; Stone, R. E.: The linear complementarity problem. (1992) · Zbl 0757.90078
[16] Crank, J.: Free and moving boundary problems. (1984) · Zbl 0547.35001
[17] Dafermos, S.: An iterative scheme for variational inequalities. Math. program. 26, 40-47 (1983) · Zbl 0506.65026
[18] Dafermos, S.: Sensitivity analysis in variational inequalities. Math. oper. Res. 13, 421-434 (1988) · Zbl 0674.49007
[19] Demyanov, V. F.; Stavroulakis, G. E.; Polyakova, L. N.; Panagiotoulos, P. D.: Quasidifferentiability and nonsmooth modeling in mechanics, engineering and economics. (1996)
[20] Ding, X. P.: Perturbed proximal point algorithms for generalized quasi variational inclusions. J. math. Anal. appl. 210, 88-101 (1997) · Zbl 0902.49010
[21] Dong, J.; Zhang, D.; Nagurney, A.: A projected dynamical systems model of general financial equilibrium with stability analysis. Math. comput. Modell. 24, No. 2, 35-44 (1996) · Zbl 0858.90020
[22] Dupuis, P.; Nagurney, A.: Dynamical systems and variational inequalities. Ann. oper. Res. 44, 19-42 (1993) · Zbl 0785.93044
[23] Duvaut, G.; Lions, J. L.: Inequalities in mechanics and physics. (1976) · Zbl 0331.35002
[24] Ekeland, I.; Temam, R.: Convex analysis and variational problems. (1976) · Zbl 0322.90046
[25] El Farouq, N.: Pseudomonotone variational inequalities: convergence of proximal methods. J. optim. Theory appl. 109, 311-326 (2001) · Zbl 0993.49006
[26] Fichera, G.: Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambique condizione al controno. Atti. acad. Naz. lincei. Mem. cl. Sci. nat. Sez. ia 7, No. 8, 91-140 (1963/1964) · Zbl 0146.21204
[27] V.M. Filippov, Variational Principles for Nonpotential Operators, Vol. 77, American Math. Soc, USA, 1989 · Zbl 0682.35006
[28] Friesz, T. L.; Bernstein, D. H.; Mehta, N. J.; Ganjliazadeh, S.: Day-to-day dynamic network disequilibria and idealized traveler information systems. Oper. res. 42, 1120-1136 (1994) · Zbl 0823.90037
[29] Friesz, T. L.; Bernstein, D. H.; Stough, R.: Dynamic systems, variational inequalities and control theoretic models for predicting time-varying urban network flows. Trans. sci. 30, 14-31 (1996) · Zbl 0849.90061
[30] Fukushima, M.: Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math. program. 53, 99-110 (1992) · Zbl 0756.90081
[31] Giannessi, F.; Maugeri, A.: Variational inequalities and network equilibrium problems. (1995) · Zbl 0834.00044
[32] Giannessi, F.; Maugeri, A.; Pardalos, P. M.: Equilibrium problems: nonsmooth optimization and variational inequality models. (2001) · Zbl 0979.00025
[33] Glowinski, G.: Numerical methods for nonlinear variational problems. (1984) · Zbl 0536.65054
[34] Glowinski, R.; Lions, J. J.; Tremolieres, R.: Numerical analysis of variational inequalities. (1981) · Zbl 0463.65046
[35] Glowinski, R.; Le Tallec, P.: Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. (1989) · Zbl 0698.73001
[36] Goeleven, D.; Mantague, D.: Well-posed hemivariational inequalities. Numer. funct. Anal. optim. 16, 909-921 (1995) · Zbl 0848.49013
[37] Han, D.; Lo, H. K.: Two new self-adaptive projection methods for variational inequality problems. Comput. math. Appl. 43, 1529-1537 (2002) · Zbl 1012.65064
[38] Harker, P. T.; Pang, J. S.: Finite dimensional variational inequalities and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. program. 48, 161-220 (1990) · Zbl 0734.90098
[39] Haubruge, S.; Nguyen, V. H.; Strodiot, J. J.: Convergence analysis and applications of the glowinski-le tallec splitting method for finding a zero of the sum of two maximal monotone operators. J. optim. Theory appl. 97, 645-673 (1998) · Zbl 0908.90209
[40] B.S. He, A class of new methods for variational inequalities, Report 95, Institute of Mathematics, Nanjing University, Nanjing, PR China, 1995
[41] He, B. S.: A class of projection and contraction methods for variational inequalities. Appl. math. Optim. 35, 69-76 (1997) · Zbl 0865.90119
[42] He, B. S.: Inexact implicit methods for monotone general variational inequalities. Math. program. 86, 199-217 (1999) · Zbl 0979.49006
[43] He, B. S.; Liao, L. Z.: Improvement of some projection methods for monotone nonlinear variational inequalities. J. optim. Theory appl. 112, 111-128 (2002) · Zbl 1025.65036
[44] Iusem, A. N.; Svaiter, B. F.: A variant of korpelevich’s method for variational inequalities with a new strategy. Optimization 42, 309-321 (1997) · Zbl 0891.90135
[45] Kikuchi, N.; Oden, J. T.: Contact problems in elasticity. (1988) · Zbl 0685.73002
[46] Kinderlehrer, D.; Stampacchia, G.: An introduction to variational inequalities and their applications. (2000) · Zbl 0988.49003
[47] Korpelevich, G. M.: The extragradient method for finding saddle points and other problems. Matecon 12, 747-756 (1976) · Zbl 0342.90044
[48] Kyparisis, J.: Sensitivity analysis framework for variational inequalities. Math. program. 38, 203-213 (1987)
[49] Kyparisis, J.: Sensitivity analysis for variational inequalities and nonlinear complementarity problems. Ann. oper. Res. 27, 143-174 (1990) · Zbl 0723.90075
[50] Larsson, T.; Patriksson, M.: A class of gap functions for variational inequalities. Math. program. 64, 53-79 (1994) · Zbl 0819.65101
[51] Lewy, H.; Stampacchia, G.: On the regularity of the solutions of the variational inequalities. Commun. pure appl. Math. 22, 153-188 (1969) · Zbl 0167.11501
[52] Lions, J. L.; Stampacchia, G.: Variational inequalities. Commun. pure appl. Math. 20, 493-512 (1967) · Zbl 0152.34601
[53] Lions, P. L.; Mercier, B.: Splitting algorithms for the sum of two monotone operators. SIAM J. Numer. anal. 16, 964-979 (1979) · Zbl 0426.65050
[54] Liu, J.: Sensitivity analysis in nonlinear programs and variational inequalities via continuous selection. SIAM J. Control optim. 33, 1040-1068 (1995) · Zbl 0839.49017
[55] Luc, D. H.: Fréchet approximate Jacobians and local uniqueness of solutions in variational inequalities. J. math. Anal. appl. 268, 629-646 (2002) · Zbl 1012.49009
[56] Luc, D. T.; Noor, M. Aslam: Local uniqueness of solutions of general variational inequalities. J. optim. Theory appl. 117, 103-119 (2003) · Zbl 1030.49005
[57] Lucchetti, R.; Patrone, F.: A characterization of tykhonov well-posedness for minimum problems with applications to variational inequalities. Numer. funct. Anal. optim. 3, 461-476 (1981) · Zbl 0479.49025
[58] Lucchetti, R.; Patrone, F.: Some properties of well-posed variational inequalities governed by linear operators. Numer. funct. Anal. optim. 5, 349-361 (1982/1983) · Zbl 0517.49007
[59] Luo, Z. Q.; Tseng, P.: Error bounds and convergence analysis of feasible decent methods: a general approach. Ann. oper. Res. 46, 157-178 (1993) · Zbl 0793.90076
[60] U. Mosco, Implicit variational problems and quasi variational inequalities, Lecture Notes Math. 543, Springer-Verlag, Berlin, Berlin, 1976, pp. 83--126 · Zbl 0346.49003
[61] Martinet, B.: Regularization d’inequations variationnelles par approximations successive. Revue fran. D’informat. rech. Oper. 4, 154-159 (1970)
[62] Moudafi, A.; Thera, M.: Finding a zero of the sum of two maximal monotone operators. J. optim. Theory appl. 94, 425-448 (1994)
[63] Moudafi, A.; Noor, M. Aslam: Sensitivity analysis for variational inclusions by Wiener--Hopf equations technique. J. appl. Math. stochastic anal. 12, 223-232 (1999) · Zbl 0946.49008
[64] Nagurney, A.: Network economics, A variational inequality approach. (1999) · Zbl 0873.90015
[65] Nagurney, A.; Zhang, D.: Projected dynamical systems and variational inequalities with applications. (1996) · Zbl 0865.90018
[66] M. Aslam Noor, The Riesz-Frechet Theorem and Monotonicity, M.Sc. Thesis, Queen’s University, Kingston, Canada, 1971
[67] Noor, M. Aslam: Bilinear forms and convex set in Hilbert space. Boll. union. Math. ital. 5, 241-244 (1972) · Zbl 0261.49006
[68] M. Aslam Noor, On Variational Inequalities, Ph.D. Thesis, Brunel University, London, UK, 1975
[69] Noor, M. Aslam: Strongly nonlinear variational inequalities. C. R. Math. rep. 4, 213-218 (1982) · Zbl 0502.49008
[70] Noor, M. Aslam: Fixed-point approach for complementarity problems. Math. anal. Appl. 133, 437-448 (1988) · Zbl 0649.65037
[71] Noor, M. Aslam: General variational inequalities. Appl. math. Lett. 1, 119-121 (1988) · Zbl 0655.49005
[72] Noor, M. Aslam: Quasi variational inequalities. Appl. math. Lett. 1, 367-370 (1988) · Zbl 0708.49015
[73] Noor, M. Aslam: Some classes of variational inequalities. Constantin Carathéodory: an international tribute, 996-1019 (1991) · Zbl 0747.49011
[74] Noor, M. Aslam: Generalized Wiener--Hopf equations and nonlinear quasi variational inequalities. Pan amer. Math. J. 2, No. 4, 51-70 (1992) · Zbl 0842.49011
[75] Noor, M. Aslam: Wiener--Hopf equations and variational inequalities. J. optim. Theory appl. 79, 197-206 (1993) · Zbl 0799.49010
[76] Noor, M. Aslam: Some iterative techniques for variational inequalities. Optimization 46, 391-401 (1999) · Zbl 0966.49010
[77] Noor, M. Aslam: Variational inequalities in physical oceanography. Ocean wave engineering, 201-226 (1994)
[78] Noor, M. Aslam: Sensitivity analysis for quasi variational inequalities. J. optim. Theory appl. 95, 399-407 (1997) · Zbl 0896.49003
[79] Noor, M. Aslam: Wiener--Hopf equations techniques for variational inequalities. Korean J. Comput. appl. Math. 7, 581-599 (2000) · Zbl 0978.49011
[80] Noor, M. Aslam: Some recent advances in variational inequalities, part I, basic concepts. New Zealand J. Math. 26, 53-80 (1997) · Zbl 0886.49004
[81] Noor, M. Aslam: Some recent advances in variational inequalities, part II, other concepts. New Zealand J. Math. 26, 229-255 (1997) · Zbl 0889.49006
[82] Noor, M. Aslam: Generalized quasi variational inequalities and implicit Wiener--Hopf equations. Optimization 45, 197-222 (1999) · Zbl 0939.49009
[83] Noor, M. Aslam: New approximation schemes for general variational inequalities. J. math. Anal. appl. 251, 217-229 (2000) · Zbl 0964.49007
[84] Noor, M. Aslam: Three-step iterative algorithms for multivalued quasi variational inclusions. J. math. Anal. appl. 255, 589-604 (2001) · Zbl 0986.49006
[85] Noor, M. Aslam: Modified resolvent algorithms for general mixed variational inequalities. J. comput. Appl. math. 135, 111-124 (2001) · Zbl 0997.65091
[86] Noor, M. Aslam: Projection-splitting algorithms for general monotone variational inequalities. J. comput. Anal. appl. 4, 47-61 (2002) · Zbl 1039.49010
[87] Noor, M. Aslam: Proximal methods for mixed variational inequalities. J. optim. Theory appl. 115, 447-451 (2002) · Zbl 1033.49014
[88] Noor, M. Aslam: Operator-splitting methods for general mixed variational inequalities. J. inequal. Pure appl. Math. 3, No. 4 (2002) · Zbl 1039.49008
[89] Noor, M. Aslam: Extragradient method for pseudomonotone variational inequalities. J. optim. Theory appl. 117, 475-488 (2003) · Zbl 1049.49009
[90] Noor, M. Aslam: Implicit dynamical systems and quasi variational inequalities. Appl. math. Comput. 134, 69-81 (2002) · Zbl 1032.47041
[91] Noor, M. Aslam: Implicit resolvent dynamical systems for quasi variational inclusions. J. math. Anal. appl. 269, 216-226 (2002) · Zbl 1002.49010
[92] Noor, M. Aslam: Sensitivity analysis framework for general quasi variational inequalities. Comput. math. Appl. 44, 1175-1181 (2002) · Zbl 1034.49007
[93] Noor, M. Aslam: New extragradient-type methods for general variational inequalities. J. math. Anal. appl. 277, 379-395 (2003) · Zbl 1033.49015
[94] M. Aslam Noor, Theory of general variational inequalities, Preprint, Etisalat College of Engineering, Sharjah, UAE, 2003
[95] Noor, M. Aslam: A modified extragradient method for general monotone variational inequalities. Comput. math. Appl. 38, 19-24 (1999) · Zbl 0939.47055
[96] Noor, M. Aslam: Some algorithms for general monotone mixed variational inequalities. Math. comput. Modell. 29, 1-9 (1999) · Zbl 0991.49004
[97] Noor, M. Aslam: Set-valued mixed quasi variational inequalities and implicit resolvent equations. Math. comput. Modell. 29, 1-11 (1999) · Zbl 0994.47063
[98] Noor, M. Aslam: A class of new iterative methods for general mixed variational inequalities. Math. computer modell. 31, No. 13, 11-19 (2001)
[99] Noor, M. Aslam: A predictor--corrector method for general variational inequalities. Appl. math. Lett. 14, 53-87 (2001) · Zbl 0972.49006
[100] Noor, M. Aslam: Merit functions for variational-like inequalities. Math. inequal. Appl. 3, 117-128 (2000) · Zbl 0966.49009
[101] Noor, M. Aslam: A Wiener--Hopf dynamical system for variational inequalities. New Zealand J. Math. 31, 173-182 (2002) · Zbl 1047.49011
[102] Noor, M. Aslam: Well-posed variational inequalities. J. appl. Math. comput. 11, 165-172 (2003) · Zbl 1033.49016
[103] Noor, M. Aslam: Mixed quasi variational inequalities. Appl. math. Comput. (2003) · Zbl 1035.65063
[104] Noor, M. Aslam; Oettli, W.: On general nonlinear complementarity problems and quasi equilibria. Le matemat. 49, 313-331 (1994) · Zbl 0839.90124
[105] Noor, M. Aslam; Noor, K. Inayat: Multivalued variational inequalities and resolvent equations. Math. comput. Modell. 26, No. 4, 109-121 (1997) · Zbl 0893.49005
[106] Noor, M. Aslam; Noor, K. Inayat: Sensitivity analysis for quasi variational inclusions. J. math. Anal. appl. 236, 290-299 (1999) · Zbl 0949.49007
[107] Noor, M. Aslam; Noor, K. Inayat: Inertial proximal methods for mixed quasi variational inequalities. Nonlin. funct. Anal. appl. 8 (2003) · Zbl 1035.65063
[108] M. Aslam Noor, K. Inayat Noor, Self-adaptive projection algorithms for general variational inequalities, Appl. Math. Comput., submitted for publication
[109] Noor, M. Aslam; Al-Said, E.: Change of variable method for generalized complementarity problems. J. optim. Theory appl. 100, 389-395 (1999) · Zbl 0915.90244
[110] Noor, M. Aslam; Al-Said, E. A.: Finite difference method for a system of third-order boundary value problems. J. optim. Theory appl. 112, 627-637 (2002) · Zbl 1002.49012
[111] Noor, M. Aslam; Rassias, T. M.: A class of projection methods for general variational inequalities. J. math. Anal. appl. 268, 334-343 (2002) · Zbl 1038.49017
[112] Noor, M. Aslam; Noor, K. Inayat; Rassias, T. M.: Some aspects of variational inequalities. J. comput. Appl. math. 47, 285-312 (1993) · Zbl 0788.65074
[113] Noor, M. Aslam; Noor, K. Inayat; Rassias, T. M.: Invitation to variational inequalities. Analysis, geometry and groups: A Riemann legacy volume, 373-448 (1993) · Zbl 0913.49006
[114] Noor, M. Aslam; Noor, K. Inayat; Rassias, T. M.: Set-valued resolvent equations and mixed variational inequalities. J. math. Anal. appl. 220, 741-759 (1998) · Zbl 1021.49002
[115] Noor, M. Aslam; Tirmizi, S. I. A.: Finite difference techniques for solving obstacle problems. Appl. math. Lett. 1, 267-271 (1988) · Zbl 0659.49006
[116] Noor, M. Aslam; Wang, Y. J.; Xiu, N. H.: Some projection iterative schemes for general variational inequalities. J. inequal. Pure appl. Math. 3, No. 3, 1-8 (2002) · Zbl 1142.49304
[117] Noor, M. Aslam; Wang, Y. J.; Xiu, N. H.: Some new projection methods for variational inequalities. Appl. math. Comput. 137, 423-435 (2003) · Zbl 1031.65078
[118] Pang, J. S.; Yao, J. C.: On a generalization of a normal map and equation. SIAM J. Control optim. 33, 168-184 (1995) · Zbl 0827.90131
[119] Pappalardo, M.; Passacantando, M.: Stability for equilibrium problems: from variational inequalities to dynamical systems. J. optim. Theory appl. 113, 567-582 (2002) · Zbl 1017.49013
[120] Patriksson, M.: Nonlinear programming and variational inequalities: A unified approach. (1998) · Zbl 0912.90261
[121] Pitonyak, A.; Shi, P.; Shiller, M.: On an iterative method for variational inequalities. Numer. math. 58, 231-242 (1990) · Zbl 0689.65043
[122] Polyak, B. T.: Some methods of speeding up the convergence of iterative methods. USSR comput. Math. math. Phys. 4, 1-17 (1964)
[123] Polyak, B. T.: Introduction to optimization. (1987) · Zbl 0708.90083
[124] Qiu, Y.; Magnanti, T. L.: Sensitivity analysis for variational inequalities defined on polyhedral sets. Math. oper. Res. 14, 410-432 (1989) · Zbl 0698.90069
[125] Robinson, S. M.: Normal maps induced by linear transformations. Math. oper. Res. 17, 691-714 (1992) · Zbl 0777.90063
[126] Rockafellar, R. T.: Monotone operators and the proximal point algorithms. SIAM J. Control optim. 14, 877-898 (1976) · Zbl 0358.90053
[127] Shi, P.: Equivalence of variational inequalities with Wiener--Hopf equations. Proc. amer. Math. soc. 111, 339-346 (1991) · Zbl 0881.35049
[128] Sibony, M.: Methodes iteratives pour LES equations et inequations aux derivees partielles nonlineaires de type monotone. Calcolo 7, 65-183 (1970) · Zbl 0225.35010
[129] Solodov, M. V.; Svaiter, B. F.: A new projection method for variational inequality problems. SIAM J. Control optim. 42, 309-321 (1997) · Zbl 0891.90135
[130] Solodov, M. V.; Tseng, P.: Modified projection type methods for monotone variational inequalities. SIAM J. Control optim. 34, 1814-1830 (1996) · Zbl 0866.49018
[131] Stampacchia, G.: Formes bilineaires coercivites sur LES ensembles convexes. C. R. Acad. Paris 258, 4413-4416 (1964) · Zbl 0124.06401
[132] Sun, D.: A class of iterative methods for solving nonlinear projection equations. J. optim. Theory appl. 91, 123-140 (1996) · Zbl 0871.90091
[133] Sun, D.: A projection and contraction method for the nonlinear complementarity problem and its extensions. Math. numer. Sin. 16, 183-194 (1994) · Zbl 0900.65188
[134] Tonti, E.: Variational formulation for every nonlinear problem. Int. J. Engng. sci. 22, 1343-1371 (1984) · Zbl 0558.49022
[135] Tobin, R. L.: Sensitivity analysis for variational inequalities. J. optim. Theory appl. 48, 191-204 (1986) · Zbl 0557.49004
[136] Tseng, P.: A modified forward--backward splitting method for maximal monotone mappings. SIAM J. Control optim. 38, 431-446 (2000) · Zbl 0997.90062
[137] Tseng, P.: On linear convergence of iterative methods for variational inequality problem. J. comput. Appl. math. 60, 237-252 (1995) · Zbl 0835.65087
[138] Uko, L. U.: Strongly nonlinear general equations. J. math. Anal. appl. 220, 65-76 (1998) · Zbl 0918.49007
[139] Wang, Y. J.; Xiu, N. H.; Wang, C. Y.: Unified framework of projection methods for pseudomonotone variational inequalities. J. optim. Theory appl. 111, 643-658 (2001) · Zbl 1039.49014
[140] Wang, Y. J.; Xiu, N. H.; Wang, C. Y.: A new version of extragradient projection method for variational inequalities. Comput. math. Appl. 42, 969-979 (2001) · Zbl 0993.49005
[141] Xia, Y. S.; Wang, J.: On the stability of globally projected dynamical systems. J. optim. Theory appl. 106, 129-150 (2000) · Zbl 0971.37013
[142] Xiu, N.; Zhang, J.; Noor, M. Aslam: Tangent projection equations and general variational equalities. J. math. Anal. appl. 258, 755-762 (2001) · Zbl 1008.49010
[143] Xiu, N. H.; Zhang, J.: Some recent advances in projection-type methods for variational inequalities. J. comput. Appl. math. 152, 559-585 (2003) · Zbl 1018.65083
[144] Xiu, N. H.; Zhang, J. Z.: Global projection-type error bounds for general variational inequalities. J. optim. Theory appl. 112, 213-228 (2002) · Zbl 1005.49004
[145] Xiu, N. M.; Zhang, J.: Local convergence of projection-type algorithms: a unified approach. J. optim. Theory appl. 115, 211-230 (2002) · Zbl 1091.49011
[146] Yen, N. D.: Holder continuity of solutions to a parametric variational inequality. Appl. math. Optim. 31, 245-255 (1995) · Zbl 0821.49011
[147] Yen, N. D.; Lee, G. M.: Solution sensitivity of a class of variational inequalities. J. math. Anal. appl. 215, 46-55 (1997) · Zbl 0906.49002
[148] Zhang, D.; Nagurney, A.: On the stability of the projected dynamical systems. J. optim. Theory appl. 85, 97-124 (1995) · Zbl 0837.93063
[149] Zhao, Y. B.: Extended projection methods for monotone variational inequalities. J. optim. Theory appl. 100, 219-231 (1999) · Zbl 0922.90137
[150] Zhu, D. L.; Marcotte, P.: Cocoercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM J. Optim. 6, 714-726 (1996) · Zbl 0855.47043