Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings

S. S. Chang; Salahuddin; M. Liu; X. R. Wang; J. F. Tang; S. S. Chang; Salahuddin; M. Liu; X. R. Wang; J. F. Tang

doi:10.3934/math.2021108

AIMS Mathematics

2021, Volume 6, Issue 2: 1800-1815. doi: 10.3934/math.2021108

Previous Article Next Article

Research article

Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings

1.
Center for General Education, China Medical University, Taichung, 40402, Taiwan
2.
Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia
3.
Department of Mathematics, Yibin University, Yibin, Sichuan, China

Received: 11 September 2020 Accepted: 08 November 2020 Published: 30 November 2020
MSC : 49J40, 47H09, 47J20, 54H25

The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.
Citation: S. S. Chang, Salahuddin, M. Liu, X. R. Wang, J. F. Tang. Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings[J]. AIMS Mathematics, 2021, 6(2): 1800-1815. doi: 10.3934/math.2021108

Related Papers:

Abstract

The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.

References

[1]	X. Li, X. S. Li, N. J. Huang, A generalized f-projection algorithm for inverse mixed variational inequalities, Optim. Lett., 8 (2014), 1063-1076. doi: 10.1007/s11590-013-0635-4
[2]	G. Y. Chen, C. J. Goh, X. Q. Yang, On gap functions for vector variational inequalities. In: F. Giannessi, (ed.), Vector variational inequalities and vector equilibria: mathematical theories, Kluwer Academic Publishers, Boston, 2000.
[3]	X. Q. Yang, J. C. Yao, Gap functions and existence of solutions to set-valued vector variational inequalities, J. Optim. Theory Appl., 115 (2002), 407-417. doi: 10.1023/A:1020844423345
[4]	Salahuddin, Regularization techniques for Inverse variational inequalities involving relaxed cocoercive mapping in Hilbert spaces, Nonlinear Anal. Forum, 19 (2014), 65-76.
[5]	S. J. Li, H. Yan, G. Y. Chen, Differential and sensitivity properties of gap functions for vector variational inequalities, Math. Methods Oper. Res., 57 (2003), 377-391. doi: 10.1007/s001860200254
[6]	M. V. Solodov, Merit functions and error bounds for generalized variational inequalities, J. Math. Anal. Appl., 287 (2003), 405-414. doi: 10.1016/S0022-247X(02)00554-1
[7]	D. Aussel, R. Gupta, A. Mehra, Gap functions and error bounds for inverse quasi-variational inequality problems, J. Math. Anal. Appl., 407 (2013), 270-280. doi: 10.1016/j.jmaa.2013.03.049
[8]	B. S. Lee, Salahuddin, Minty lemma for inverted vector variational inequalities, Optimization, 66 (2017), 351-359. doi: 10.1080/02331934.2016.1271799
[9]	J. Chen, E. Kobis, J. C. Yao, Optimality conditions for solutions of constrained inverse vector variational inequalities by means of nonlinear scalarization, J. Nonlinear Var. Anal., 1 (2017), 145-158.
[10]	X. K. Sun, Y. Chai, Gap functions and error bounds for generalized vector variational inequalities, Optim. Lett., 8 (2014), 1663-1673. doi: 10.1007/s11590-013-0685-7
[11]	K. Q. Wu, N. J. Huang, The generalised f-projection operator with an application, Bull. Aust. Math. Soc., 73 (2006), 307-317. doi: 10.1017/S0004972700038892
[12]	C. Q. Li, J. Li, Merit functions and error bounds for constrained mixed set-valued variational inequalities via generalized $f$-projection operators, Optimization, 65 (2016), 1569-1584. doi: 10.1080/02331934.2016.1163555
[13]	S. S. Chang, Salahuddin, L. Wang, G. Wang, Z. L. Ma, Error bounds for mixed set-valued vector inverse quasi variational inequalities, J. Inequal Appl., 2020:160 (2020), 1-16.
[14]	Z. B. Wang, Z. Y. Chen, Z. Chen, Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems, Fixed Point Theory Appl., 2019:14 (2019), 1-14. doi: 10.17654/FP014010001
[15]	F. Giannessi, Vector variational inequalities and vector equilibria: mathematical theories, Kluwer Academic Publishers/Boston/London, Dordrecht, 2000.
[16]	Salahuddin, Solutions of vector variational inequality problems, Korean J. Math., 26 (2018), 299-306.
[17]	X. Li, Y. Z. Zou, Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities, J. Inequal. Appl., 2016 (2016), 1-13. doi: 10.1186/s13660-015-0952-5

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)