A study of multivalued variational inequalities via horizon maps and graphical convergence

References

• Auslender A, Teboulle M. Asymptotic cones and functions in optimization and variational inequalities. New York: Springer; 2003.
   Google Scholar
• Gowda SM, Pang JS. Some existence results for multivalued complementarity problems. Math Oper Res. 1992;17:657–669.
   Web of Science ®Google Scholar
• Borwein JM, Lewis A. Convex analysis and nonlinear optimization. New York (NY): Springer; 2006.
   Google Scholar
• Crouzeix JP. Pseudomonotone variational inequality problems: existence of solutions. Math Program. 1997;78:305–314.
   Web of Science ®Google Scholar
• Daniilidis A, Hadjisavvas N. Coercivity conditions and variational inequalities. Math Program. 1999;86:433–438.
   Web of Science ®Google Scholar
• Flores-Bazán F, López R. Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems. ESAIM Control Optim Calc Var. 2006;12:271–293.
   Web of Science ®Google Scholar
• Kien BT, Wong MM, Wong NC, et al. Degree theory for generalized variational inequalities and applications. Eur J Oper Res. 2009;192:730–736.
   Web of Science ®Google Scholar
• Qiao F, He Y. Strict feasibility of pseudomonotone set-valued variational inequalities. Optimization. 2011;60:303–310.
   Web of Science ®Google Scholar
• Bianchi M, Hadjisavvas N, Schaible S. Exceptional families of elements for variational inequalities in Banach spaces. J Optim Theory Appl. 2006;129:23–31.
   Web of Science ®Google Scholar
• Fan JH, Wang XG. Solvability of generalized variational inequality problems for unbounded sets in reflexive Banach spaces. J Optim Theory Appl. 2009;143:59–74.
   Web of Science ®Google Scholar
• Ansari QH, Lalitha CS, Mehta M. Generalized convexity, nonsmooth variational inequalities, and nonsmooth optimization. Boca Raton (FL): Taylor & Francis; 2014.
   Google Scholar
• Rockafellar RT, Wets RJ. Variational analysis. Berlin: Springer; 1998.
   Google Scholar
• López R, Sama M. Horizon maps and graphical convergence revisited. SIAM J Optim. 2021;31:1330–1351.
   Web of Science ®Google Scholar
• Lignola MB, Morgan J. Generalized variational inequalities with pseudomonotone operators under perturbations. J Optim Theory Appl. 1999;101:213–220.
   Web of Science ®Google Scholar
• Morgan J, Romianello M. Generalized quasi-variational inequalities: duality under perturbations. J Math Anal Appl. 2006;324:773–784.
   Web of Science ®Google Scholar
• Aubin JP, Frankowska H. Set-valued analysis. Boston (MA): Birkhäuser; 1990.
   Google Scholar
• Hu S, Papageorgiou NS. Handbook of multivalued analysis. Volume I: theory. Berlin: Springer; 1997.
   Google Scholar
• Attouch H. Variational convergence for functions and operators. Boston (MA): Pitman; 1984.
   Google Scholar
• Cianciaruso F, Marino G, Muglia L, et al. Notes on graph convergence for maximal monotone operators. Bull Aust Math Soc. 2011;83:22–29.
   Web of Science ®Google Scholar
• Li FL, He Y. Solvability of a perturbed variational inequality. Pac J Optim. 2014;10:105–111.
   Web of Science ®Google Scholar
• Wang M. Existence theorems for perturbed variational inequalities in Banach spaces. J Fixed Point Theory Appl. 2018;20:55.
   Web of Science ®Google Scholar
• Aubin JP, Cellina A. Differential inclusions. Berlin: Springer; 1984.
   Google Scholar
• Borwein JM, Zhu QJ. Techniques of variational analysis. New York (NY): Springer; 2005.
   Google Scholar
• Burachik R, Iusem A. Set-valued mappings and enlargements of monotone operators. New York (NY): Springer; 2008.
   Google Scholar
• Borwein JM. Adjoint process duality. Math Oper Res. 1983;8:403–434.
   Web of Science ®Google Scholar
• Luc DT. Theory of vector optimization. Berlin: Springer; 1989.
   Google Scholar
• Attouch H, Chbani Z, Moudafi A. Recession operators and solvability of variational problems in reflexive Banach spaces. In: Bouchitté G. editor. Calculus of variations, homogenization and continuous mechanics. River Edge (NJ): World Scientific; 1994. p. 51–67.
   Google Scholar
• Moudafi A, Maingé PE. Towards viscosity approximations of hierarchical fixed-point problems. Fixed Point Theory Appl. 2006:1–10. Article 95453.
   Google Scholar