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Stability analysis for set-valued inverse mixed variational inequalities in reflexive Banach spaces. (English) Zbl 1537.49012

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49K40 Sensitivity, stability, well-posedness
49N45 Inverse problems in optimal control

References:

[1] Facchinei, F.; Pang, J. S., Finite-Dimensional Variational Inequalities and Complementarity Problems (2003), Berlin: Springer, Berlin · Zbl 1062.90001
[2] Xiao, Y. B.; Liu, M. T.; Chen, T.; Huang, N. J., Stability analysis for evolutionary variational-hemivariational inequalities with constraint sets, Sci. China Math., 65, 7, 1469-1484 (2022) · Zbl 1519.47067 · doi:10.1007/s11425-020-1838-2
[3] Zhong, R. Y.; Huang, N. J., Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces, J. Optim. Theory Appl., 152, 3, 696-709 (2012) · Zbl 1238.49023 · doi:10.1007/s10957-011-9914-3
[4] Ju, X. X.; Li, C.; He, X.; Gang, F., A proximal neurodynamic model for solving inverse mixed variational inequalities, Neural Netw., 138, 1-9 (2021) · Zbl 1523.49011 · doi:10.1016/j.neunet.2021.01.012
[5] Chen, J. W.; Ju, X. X.; Kobis, E.; Liou, Y. C., Tikhonov type regularization methods for inverse mixed variational inequalities, Optimization, 69, 2, 401-413 (2020) · Zbl 1432.49006 · doi:10.1080/02331934.2019.1607339
[6] Baiocchi, C.; Buttazzo, G.; Gastaldi, F.; Tomarelli, F., General existence theorems for unilateral problems in continuum mechanics, Arch. Ration. Mech. Anal., 100, 149-189 (1988) · Zbl 0646.73011 · doi:10.1007/BF00282202
[7] Adly, S.; Ernst, E.; Théra, M., Stability of the solution set of non-coercive variational inequalities, Commun. Contemp. Math., 4, 1, 145-160 (2002) · Zbl 1012.47052 · doi:10.1142/S0219199702000579
[8] McLinden, L., Stable monotone variational inequalities, Math. Program., 48, 303-338 (1990) · Zbl 0726.90093 · doi:10.1007/BF01582261
[9] Addi, K.; Adly, S.; Goeleven, D.; Saoud, H., A sensitivity analysis of a class of semi-coercive variational inequalities using recession tools, J. Glob. Optim., 40, 7-27 (2008) · Zbl 1295.49018 · doi:10.1007/s10898-007-9207-4
[10] He, Y. R., Stable pseudomonotone variational inequality in reflexive Banach spaces, J. Math. Anal. Appl., 330, 1, 352-363 (2007) · Zbl 1124.49005 · doi:10.1016/j.jmaa.2006.07.063
[11] Fan, J. H.; Zhong, R. Y., Stability analysis for variational inequality in reflexive Banach spaces, Nonlinear Anal., 69, 8, 2566-2574 (2008) · Zbl 1172.49010 · doi:10.1016/j.na.2007.08.031
[12] Zhong, R. Y.; Huang, N. J., Stability analysis for Minty mixed variational inequality in reflexive Banach spaces, J. Optim. Theory Appl., 147, 3, 454-472 (2010) · Zbl 1218.49032 · doi:10.1007/s10957-010-9732-z
[13] Yang, J. F., Dynamic power price problem: an inverse variational inequality approach, J. Ind. Manag. Optim., 4, 4, 673-684 (2008) · Zbl 1157.91421 · doi:10.3934/jimo.2008.4.673
[14] He, B. S.; He, X. Z.; Liu, H. X., Solving a class of constrained ‘black-box’ inverse variational inequalities, Eur. J. Oper. Res., 204, 3, 391-401 (2010) · Zbl 1181.91148 · doi:10.1016/j.ejor.2009.07.006
[15] Scrimali, L., An inverse variational inequality approach to the evolutionary spatial price equilibrium problem, Optim. Eng., 13, 3, 375-387 (2012) · Zbl 1293.91116 · doi:10.1007/s11081-011-9152-4
[16] Li, X.; Li, X. S.; Huang, N. J., A generalized f-projection algorithm for inverse mixed variational inequalities, Optim. Lett., 8, 3, 1063-1076 (2014) · Zbl 1321.90138 · doi:10.1007/s11590-013-0635-4
[17] Barbagallo, A.; Mauro, P., Inverse variational inequality approach and applications, Numer. Funct. Anal. Optim., 35, 7-9, 851-867 (2014) · Zbl 1295.49006 · doi:10.1080/01630563.2014.895751
[18] Luo, X. P., Tikhonov regularization methods for inverse variational inequalities, Optim. Lett., 8, 3, 877-887 (2014) · Zbl 1310.90113 · doi:10.1007/s11590-013-0643-4
[19] Vuong, P. T.; He, X. Z.; Thong, D. V., Global exponential stability of a neural network for inverse variational inequalities, J. Optim. Theory Appl., 190, 3, 915-930 (2021) · Zbl 07403127 · doi:10.1007/s10957-021-01915-x
[20] Xu, Y. D., Nonlinear separation approach to inverse variational inequalities, Optimization, 56, 7, 1315-1335 (2016) · Zbl 1345.49011 · doi:10.1080/02331934.2016.1149584
[21] Hu, R.; Fang, Y. P., Levitin-Polyak well-posedness by perturbations of inverse variational inequalities, Optim. Lett., 7, 2, 343-359 (2013) · Zbl 1288.90106 · doi:10.1007/s11590-011-0423-y
[22] Luo, X.P.: Stability analysis of set-valued inverse variational inequalities in reflexive Banach spaces. J. Fixed Point Theory Appl. 23(3) (2021) · Zbl 1492.47061
[23] Aussel, D.; Gupta, R.; Mehra, A., Gap functions and error bounds for inverse quasi-variational inequality problems, J. Math. Anal. Appl., 407, 2, 270-280 (2013) · Zbl 1311.49016 · doi:10.1016/j.jmaa.2013.03.049
[24] Jiang, Y. N.; Cai, X. J.; Han, D. R., Solving policy design problems: alternating direction method of multipliers-based methods for structured inverse variational inequalities, Eur. J. Oper. Res., 280, 2, 417-427 (2020) · Zbl 1430.90530 · doi:10.1016/j.ejor.2019.05.044
[25] Zhang, Y.F., Yu, G.L.: Error bounds for inverse mixed quasi-variational inequality via generalized residual gap functions. Asia-Pac. J. Oper. Res. 39(2) (2022) · Zbl 1493.49016
[26] Tangkhawiwetkul, J., A neural network for solving the generalized inverse mixed variational inequality problem in Hilbert spaces, AIMS Math., 8, 3, 7258-7276 (2023) · doi:10.3934/math.2023365
[27] Li, W.; Wang, X.; Huang, N. J., Differential inverse variational inequalities in finite dimensional spaces, Acta Math. Sci., 35, 2, 407-422 (2015) · Zbl 1340.49009 · doi:10.1016/S0252-9602(15)60012-1
[28] Zou, X. J.; Gong, D. W.; Wang, L. P.; Chen, Z. Y., A novel method to solve inverse variational inequality problems based on neural networks, Neurocomputing, 173, 3, 1163-1168 (2016) · doi:10.1016/j.neucom.2015.08.073
[29] Zhu, X. Y.; Li, W.; Luo, X. P., Stability for a class of differential set-valued inverse variational inequalities in finite dimensional spaces, Axioms, 11, 9 (2022) · doi:10.3390/axioms11090475
[30] Zalinescu, C., Convex Analysis in General Vector Spaces (2002), River Edge: World Scientific, River Edge · Zbl 1023.46003 · doi:10.1142/5021
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