خوش‌وضعی قوی برای رده‌ای از نامساوی‌های تغییراتی دو‌بخشی با نگاشت‌های مجموعه‌مقدار

نویسندگان
دانشگاه بین المللی امام خمینی (ره)، دانشکدۀ علوم پایه، گروه ریاضی محض
چکیده
در این مقاله گسترشی از خوش‌وضعی را برای سیستمی از نامساوی‌های تغییراتی چند مقداری دوبخشی که توابع درگیر نگاشت‌های مجموعه‌مقدار هستند، ارائه داده و مشخص‌سازی متریکی برای آنها به‌دست می‌آوریم. هم‌چنین نشان می‌دهیم که خوش‌وضعی قوی در این حالت معادل با وجود و یکتایی جواب برای این نامساوی‌های تغییراتی چند‌مقداری دوبخشی است.
کلیدواژه‌ها

عنوان مقاله English

Strong well-posedness for a class of split variational inequalities with set-valued maps

نویسندگان English

Mahnaz Shams
Morteza Oveisiha
Imam Khomeini International University
چکیده English

In this paper, we present a generalization of well-posedness for a system of split multi-valued variational inequalities with set-valued maps and establish a metric characterization for them. Moreover, we show that the strong well-posedness is equivalent to the existence and uniqueness of solution for a split multi-valued variational inequality../files/site1/files/72/11Abstract.pdf

کلیدواژه‌ها English

approximating sequence
well-posedness
variational inequality
normal subdifferential
1. Bao T. Q., Mordukhovich B. S., "Variational principles for set-valued mappings with applications to multiobjective optimization", Control Cyber, 36 (2007) 531-562.## 2. Censor Y., Gibali A., Reich S., "Algorithms for the split variational inequality problem", Numer. Algorithms. 59 (2012) 301-323. ## 3. Fang Y. P., Hu R., "Parametric well-posedness for variational inequalities defined by bifunctions", Comput. Math. Appl, 53 (2007) 1306-1316. ## 4. Hu R., Fang Y. P., "Characterization of Levitin-Polyak well-posedness by perturbation for the split variational inequality problem", Optimization, 65 (2016) 1717-1732. ## 5. Hu H., Xiao Y. B., Huang N. J., Wang X., "Equivalence results of well-posedness for split variational-hemivariational inequalities", J. Nonlinear Convex Anal., 20 (2019) 447-459. ## 6. Khakrah E., Razani A., Mirzaei R., Oveisiha M., "Some metric characterizations of well-posedness for hemivariational-like inequalities", J. Nonlinear Funct. Anal., (2017) Article ID 44. ## 7. Lucchetti R., Patrone F., "A characterization of Tykhonov well-posedness for minimum problems with applications to variational inequalities", Numr. Funct. Anal. Optim, 3 (1981) 461-476. ## 8. Mordukhovich B. S., "Variational Analysis and Generalized Diffierential I", Basic theory, 1st ed., ser. Grundlehren. Berlin: Springer Berlin Heidelberg, Vol. 330 (2006). ## 9. Reich S., Zaslavski A. J., "Generic well-posedness of fixed point problems", Vietnam J. Math., 46 (2017) 1-9. ## 10. Shu Q., Hu Y, R., Xiao Y. B., "Metric characterizations for well-posedness of split hemivariational inequalities", J. Ineq. Appl., 190 (2018) 1-17. ## 11. Tykhonov A. N., "On the stability of the functional optimization problem", USSR Comput. Math. Math. Phys., 6 (1966) 28-33. ## 12. Xiao Y., Huang N., "Well-posedness for a class of variational-hemivariational inqualities with perturbations", J. Optim. Theory Appl., 151 (2011) 33-51. ## 13. Xiao Y. B., Yang X., Huang N. J., "Some equivalence results for well-posedness of hemivariational inequalities", J. Global Optim., 61 (2015) 789-802. ## 14. Zeidler E., "Nonlinear Functional Analysis and its Applications", Springer, Berlin Heidelberg, Vol. II (1990). ##