Error bound analysis for split weak vector mixed quasi-variational inequality problems in fuzzy environment

References

• Auslender A. Optimisation: Méthodes numériques. Paris: Masson; 1976.
   Google Scholar
• Fukushima M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math Program. 1992;53:99–110.
   Web of Science ®Google Scholar
• Yamashita N, Fukushima M. Equivalent unconstrained minimization and global error bounds for variational inequality problems. SIAMJ Control Optim. 1997;35:273–284.
   Web of Science ®Google Scholar
• Bigi G, Passacantando M. Gap functions for quasiquilibria. J Global Optim. 2016;66:791–810.
   Web of Science ®Google Scholar
• Charitha C, Dutta J. Regularized gap functions and error bounds for vector variational inequality. Pac J Optim. 2010;6:497–510.
   Web of Science ®Google Scholar
• Fan JH, Wang XG. Gap functions and global error bounds for set-valued variational inequalities. J Comput Appl Math. 2010;233:2956–2965.
   Web of Science ®Google Scholar
• Huang NJ, Li J, Wu SY. Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings. J Global Optim. 2008;41:401–415.
   Web of Science ®Google Scholar
• Hung NV, Tam VM, Tuan N, et al. Regularized gap functions and error bounds for generalized mixed weak vector quasivariational inequality problems in fuzzy environments. Fuzzy Sets Syst. 2020;400:162–176.
   Web of Science ®Google Scholar
• Khan SA, Chen JW. Gap function and global error bounds for generalized mixed quasivariational inequalities. Appl Math Comput. 2015;260:71–81.
   Web of Science ®Google Scholar
• Khan SA, Chen JW. Gap functions and error bounds for generalized mixed vector equilibrium problems. J Optim Theory Appl. 2015;166:767–776.
   Web of Science ®Google Scholar
• Sun XK, Chai Y. Gap functions and error bounds for generalized vector variational inequalities. Optim Lett. 2014;8:1663–1673.
   Web of Science ®Google Scholar
• Solodov MV. Merit functions and error bounds for generalized variational inequalities. J Math Anal Appl. 2003;287:405–414.
   Web of Science ®Google Scholar
• Tang GJ, Huang NJ. Gap functions and global error bounds for set-valued mixed variational inequalities. Taiwanese J Math. 2013;17:1267–1286.
   Web of Science ®Google Scholar
• Xu YD, Li SJ. Gap functions and error bounds for weak vector variational inequalities. Optimization. 2014;63:1339–1352.
   Web of Science ®Google Scholar
• Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–353.
   Web of Science ®Google Scholar
• Chang SS, Zhu YG. On variational inequalities for fuzzy mappings. Fuzzy Sets Syst. 1989;32:359–367.
   Web of Science ®Google Scholar
• Chang SS. Variational inequality and complementarity problem theory with applications. Shanghai: Shanghai Scientific and Technological Literature; 1991.
   Google Scholar
• Chang SS, Huang NJ. Generalized complementarity problems for fuzzy mappings. Fuzzy Sets Syst. 1993;55:227–234.
   Web of Science ®Google Scholar
• Chang SS, Lee GM, Lee BS. textitector quasi-variational inequalities for fuzzy mappings (II). Fuzzy Sets Syst. 1999;102:333–344.
   Google Scholar
• Hung NV, Tam VM, Elisabeth K, et al. Existence of solutions and algorithm for generalized vector quasi-complementarity problems with application to traffic network problems. J Nonlinear Convex Anal. 2019;20:1751–1775.
   Web of Science ®Google Scholar
• Hung NV, Tam VM, Tuan NH, et al. Convergence analysis of solution sets for fuzzy optimization problems. J Comput Appl Math. 2020;369:112615.
   Web of Science ®Google Scholar
• Hung NV, Keller AA. Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with application to controlling traffic networks under uncertainty. Comput Appl Math. 2021;40:1–21.
   Web of Science ®Google Scholar
• Hung NV. Generalized Levitin–Polyak well–posedness for controlled systems of FMQHI-fuzzy mixed quasi-hemivariational inequalities of minty type. J Comput Appl Math. 2021;386:113263.
   Google Scholar
• Kiliçman A, Ahmad R, Rahaman M. Generalized vector complementarity problem with fuzzy mappings. Fuzzy Sets Syst. 2015;280:133–141.
   Web of Science ®Google Scholar
• Rahaman M, Ahmad R. Fuzzy vector equilibrium problem. Iran J Fuzzy Syst. 2015;12:115–122.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. algorithms for the split variational inequality problem. Numer Algorithms. 2012;59:301–323.
   Web of Science ®Google Scholar
• Byne C. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 2002;18:441–453.
   Web of Science ®Google Scholar
• Censor Y, Bortfeld T, Martin B, et al. A unified approach for inverse problem in intensity-modulated radiation therapy. Phys Med Biol. 2006;51:2352–2365.
   Web of Science ®Google Scholar
• Censor Y, Elfving T. A multiprojection algorithm using bregman projections in a product space. Numer Algorithms. 1994;8:221–239.
   Google Scholar
• Combettes PL. The convex feasibility problem in image recovery. Adv Imaging Electron Phys. 1996;95:155–270.
   Google Scholar
• He Z. The split equilibrium problems and its convergence algorithms. J Inequal Appl. 2012;162:1–15.
   Google Scholar
• Bnouhachem A. A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem. Fixed Point Theory Appl. 2014;2014:22.
   Google Scholar
• Chang SS, Wang L, Wang XR, et al. General split equality equilibrium problems with application to split optimization problems. J Optim Theory Appl. 2015;166:377–390.
   Web of Science ®Google Scholar
• Chen RD, Wang J, Zhang HW. General split equality problems in Hilbert spaces. Fixed Point Theory Appl. 2014;2014:35.
   Google Scholar
• Ma Z, Wang L, Chang SS, et al. Convergence theorems for split equality mixed equilibrium problems with applications. Fixed Point Theory Appl. 2015;2015:31.
   Google Scholar
• Kazmi KR. Split general quasi-variational inequality problem. Geo Math J. 2015;22:385–392.
   Google Scholar
• Chang SS, Wang L. Moudafi's open question and simultaneous iterative algorithm for general split equality variational inclusion problems and general split equality optimization problems. Fixed Point Theory Appl. 2014;2014:215.
   Google Scholar
• Moudafi A. Split monotone variational inclusions. J Optim Theory Appl. 2011;150:275–283.
   Web of Science ®Google Scholar
• Hu R, Fang YP. Characterizations of Levitin–Polyak well-posedness by perturbations for the split variational inequality problem. Optimization. 2016;65:1717–1732.
   Web of Science ®Google Scholar
• Hu R, Fang YP. Well-posedness of the split inverse variational inequality problem. Bull Malays Math Sci Soc. 2017;40:1733–1744.
   Web of Science ®Google Scholar
• Hung NV, Tam VM, Yao JC. Existence and convergence theorems for split general random variational inclusions with random fuzzy mappings. Linear Nonlinear Anal. 2019;5:51–65.
   Google Scholar
• Hung NV, Tam VM, Baleanu D. Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems. Math Methods Appl Sci. 2020;43:4614–4626.
   Web of Science ®Google Scholar
• Luc DT. Theory of vector optimization. Berlin: Springer-Verlag; 1989.
   Google Scholar
• Aubin JP, Ekeland I. Applied nonlinear analysis. New York: John Wiley and Sons; 1984.
   Google Scholar
• Gerstewitz Chr.. Nichtkonvexe dualitat in der vektaroptimierung. Wiss Z Der Technischen Hochsch Leuna Mersebung. 1983;25:357–364.
   Google Scholar