Properties of the Solution Set of a Class of Mixed Variational Inqualities

References

• Addi, K., Goeleven, D. (2017). Complementarity and variational inequalities in electronics. In: Daras, N., Rassias, T., eds. Operations Research, Engineering, and Cyber Security, Cham: Springer Optimization and Its Applications, Springer, pp. 1–43.
   Google Scholar
• Cottle, R. W., Pang, J. S., Stone, R. E. (2009). The Linear Complementarity Problem, Philadelphia: Society for Industrial and Applied Mathematics.
   Google Scholar
• Ferris, M. C., Pang, J. S. (1997). Engineering and economic applications of complementarity problems. SIAM Rev. 39(4):669–713. DOI: 10.1137/S0036144595285963.
   Web of Science ®Google Scholar
• Facchinei, F., Pang, J. S. (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Volumes I–II, New York: Springer.
   Google Scholar
• Konnov, I. V., Volotskaya, E. O. (2002). Mixed variational inequalities and economic equilibrium problems. J. Appl. Math. 2(6):289–314. DOI: 10.1155/S1110757X02106012.
   Google Scholar
• Browder, F. E. (1966). On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces. Proc Natl Acad Sci U S A. 56(2):419–425. DOI: 10.1073/pnas.56.2.419.
   PubMed Web of Science ®Google Scholar
• Lescarret, C. (1965). Cas d’addition des applications monotones maximales dans un espace de Hilbert. C. R. Acad. Sci. Paris. 261:1160–1163.
   Google Scholar
• Chadli, O., Gwinner, J., Ovcharova, N. (2018). On semicoercive variational-hemivariational inequalities-existence, approximation, and regularization. Vietnam J. Math. 46(2):329–342. DOI: 10.1007/s10013-018-0282-2.
   Web of Science ®Google Scholar
• Ceng, L.-C., Liou, Y.-C., Wen, C.-F., Hu, H.-Y., He, L., Cui, Y.-L. (2021). On the Hadamard well-posedness of generalized mixed variational inequalities in Banach spaces. J. Math. 2021:1–9. DOI: 10.1155/2021/9527107.
   Web of Science ®Google Scholar
• Goeleven, D. (2008). Existence and uniqueness for a linear mixed variational inequality arising in electrical circuits with transistors. J. Optim. Theory Appl. 138(3):397–406. DOI: 10.1007/s10957-008-9395-1.
   Web of Science ®Google Scholar
• Jolaoso, L. O., Shehu, Y., Yao, J.-C. (2022). Inertial extragradient type method for mixed variational inequalities without monotonicity. Math. Comput. Simul. 192:353–369. DOI: 10.1016/j.matcom.2021.09.010.
   Web of Science ®Google Scholar
• Ju, X., Che, H., Li, C., He, X. (2022). Solving mixed variational inequalities via a proximal neurodynamic network with applications. Neural Process Lett. 54(1):207–226. DOI: 10.1007/s11063-021-10628-1.
   Web of Science ®Google Scholar
• Mu, W., Fan, J. (2022). Existence results for solutions of mixed tensor variational inequalities. J Glob Optim. 82(2):389–412. DOI: 10.1007/s10898-021-01080-5.
   Web of Science ®Google Scholar
• Ovcharova, N., Gwinner, J. (2016). Semicoercive variational inequalities: from existence to numerical solutions of nonmonotone contact problems. J Optim Theory Appl. 171(2):422–439. DOI: 10.1007/s10957-016-0969-z.
   Web of Science ®Google Scholar
• Tang, G. J., Huang, N. J. (2013). Existence theorems of the variational-hemivariational inequalities. J Glob Optim. 56(2):605–622. DOI: 10.1007/s10898-012-9884-5.
   Web of Science ®Google Scholar
• Tang, G. J., Li, Y. S. (2020). Existence of solutions for mixed variational inequalities with perturbation in Banach spaces. Optim Lett. 14(3):637–651. DOI: 10.1007/s11590-018-1366-3.
   Web of Science ®Google Scholar
• Tang, G. J., Wan, Z., Huang, N. J. (2018). Strong convergence of a projection-type method for mixed variational inequalities in Hilbert spaces. Numer. Funct. Anal. Optim. 39:1–17.
   Web of Science ®Google Scholar
• Tang, G. J., Zhu, M., Liu, H. W. (2015). A new extragradient-type method for mixed variational inequalities. Oper. Res. Lett. 43(6):567–572. DOI: 10.1016/j.orl.2015.08.009.
   Web of Science ®Google Scholar
• Wang, M. (2017). The existence results and Tikhonov regularization method for generalized mixed variational inequalities in Banach spaces. Anal.Math.Phys. 7(2):151–163. DOI: 10.1007/s13324-016-0134-8.
   Web of Science ®Google Scholar
• Wang, Z., Xiao, Y., Chen, Z. (2020). Degree theory for generalized mixed quasi-variational inequalities and its applications. J Optim Theory Appl. 187(1):43–64. DOI: 10.1007/s10957-020-01748-0.
   Web of Science ®Google Scholar
• Wang, Z., Chen, Z., Xiao, Y., Zhang, C. (2020). A new projection-type method for solving multi-valued mixed variational inequalities without monotonicity. Appl. Anal. 99(9):1453–1466. DOI: 10.1080/00036811.2018.1538499.
   Web of Science ®Google Scholar
• Wang, Z. B., Huang, N. J. (2014). Exceptional family of elements for a generalized set-valued variational inequality in Banach spaces. Optimization. 63(2):167–180. DOI: 10.1080/02331934.2011.625030.
   Web of Science ®Google Scholar
• Yang, Z.-P., Lin, G.-H. (2021). Variance-based single-call proximal extragradient algorithms for stochastic mixed variational inequalities. J Optim Theory Appl. 190(2):393–427. DOI: 10.1007/s10957-021-01882-3.
   Web of Science ®Google Scholar
• Ju, X., Che, H., Li, C., He, X., Feng, G. (2021). Exponential convergence of a proximal projection neural network for mixed variational inequalities and applications. Neurocomputing. 454:54–64. DOI: 10.1016/j.neucom.2021.04.059.
   Web of Science ®Google Scholar
• Wang, Y., Huang, Z.-H., Qi, L. (2018). Global uniqueness and solvability of tensor variational inequalities. J Optim Theory Appl. 177(1):137–152. DOI: 10.1007/s10957-018-1233-5.
   Web of Science ®Google Scholar
• Iusem, A., Lara, F. (2019). Existence results for noncoercive mixed variational inequalities in finite dimensional spaces. J Optim Theory Appl. 183(1):122–138. DOI: 10.1007/s10957-019-01548-1.
   Web of Science ®Google Scholar
• Grad, S. M., Lara, F. (2021). Solving mixed variational inequalities beyond convexity. J Optim Theory Appl. 190(2):565–580. DOI: 10.1007/s10957-021-01860-9.
   Web of Science ®Google Scholar
• Iusem, A., Lara, F. (2020). A note on “Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces”. J. Optim. Theory Appl. 187(2):607–608. DOI: 10.1007/s10957-020-01722-w.
   Web of Science ®Google Scholar
• Iusem, A., Lara, F. (2022). Proximal point algorithms for quasiconvex pseudomonotone equilibrium problems. J Optim Theory Appl. 193(1–3):443–461. DOI: 10.1007/s10957-021-01951-7.
   Web of Science ®Google Scholar
• Lara, F. (2022). On Nonconvex pseudomonotone equilibrium problems with applications, Set-Valued Var. Set-Valued Var. Anal. 30(2):355–372. DOI: 10.1007/s11228-021-00586-0.
   Web of Science ®Google Scholar
• Gowda, M. S., Sossa, D. (2019). Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones. Math. Program. 177(1–2):149–171. DOI: 10.1007/s10107-018-1263-7.
   Web of Science ®Google Scholar
• Bai, X., Zheng, M., Huang, Z.-H. (2021). Unique solvability of weakly homogeneous generalized variational inequalities. J Glob Optim. 80(4):921–943. DOI: 10.1007/s10898-021-01040-z.
   Web of Science ®Google Scholar
• Ma, X.-X., Zheng, M.-M., Huang, Z.-H. (2020). A note on the nonemptiness and compactness of solution sets of weakly homogeneous variational inequalities. SIAM J. Optim. 30(1):132–148. DOI: 10.1137/19M1237478.
   Web of Science ®Google Scholar
• Zheng, M.-M., Huang, Z.-H., Bai, X.-L. (2021). Nonemptiness and compactness of solution sets to weakly homogeneous generalized variational inequalities. J Optim Theory Appl. 189(3):919–937. DOI: 10.1007/s10957-021-01866-3.
   Web of Science ®Google Scholar
• Auslender, A., Teboulle, M. (2003). Asymptotic Cones and Functions in Optimization and Variational Inequalities, New York: Springer.
   Google Scholar
• Bauschke, H. H., Combettes, P. L. (2019). Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Cham: Springer.
   Google Scholar
• Huang, Z.-H. (2003). Generalization of an existence theorem for variational inequalities. J. Optim. Theory Appl. 118(3):567–585. DOI: 10.1023/B:JOTA.0000004871.55273.15.
   Web of Science ®Google Scholar
• Saigal, R. (1976). Extension of the generalized complementarity problem. Math. OR. 1(3):260–266. DOI: 10.1287/moor.1.3.260.
   Google Scholar
• Fan, K. (1984). Some properties of convex sets related to fixed point theorems. Math. Ann. 266(4):519–537. DOI: 10.1007/BF01458545.
   Web of Science ®Google Scholar