پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 702 |
| تعداد مقالات | 10,099 |
| تعداد مشاهده مقاله | 71,318,412 |
| تعداد دریافت فایل اصل مقاله | 63,039,629 |
Relationship between nonsmooth vector optimization problem and vector variational inequalities using convexificators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 2، اردیبهشت 2024، صفحه 1-10 اصل مقاله (359.76 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28878.4093 | ||
| نویسندگان | ||
| Rohit Kumar Bhardwaj* ؛ Tirth Ram | ||
| Department of Mathematics, University of Jammu, Jammu- 180006, India | ||
| تاریخ دریافت: 17 آذر 1401، تاریخ بازنگری: 17 تیر 1402، تاریخ پذیرش: 19 تیر 1402 | ||
| چکیده | ||
| In this article, we examine a nonsmooth vector optimization problem with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type vector variational inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth vector optimization problems using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings. | ||
| کلیدواژهها | ||
| Convexificator؛ nonsmooth vector optimization problem؛ approximate efficient solutions | ||
| مراجع | ||
|
[1] D. Bhatia, A. Gupta, and P. Arora, Optimality via generalized approximate convexity and quasiefficiency, Optim. Lett. 7 (2013), 127–135. [2] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983. [3] V.F. Demyanov, Convexification and Concavification of positively homogeneous functions by the same family of linear functions, Report 3 (1994), no. 802. [4] V. F. Demyanov, Exhausters and convexificators new tools in nonsmooth analysis, editors. Quasidifferentiability and Related Topics, Kluwer Academic Publishers, Dordrecht, 2000, pp. 85–137. [5] V.F. Demyanov and V. Jeyakumar, Hunting for a smaller convex subdifferential, J. Glob. Optim. 10 (1997) 305–326. [6] M. Golestani and S. Nobakhtian, Convexificator and strong Kuhn-Tucker conditions, Comput. Math. Appl. 64 (2012), 550–557. [7] D. Gupta and A. Mehra, Two types of approximate saddle points, Numer. Funct. Anal. Optim. 29 (2008), 532–550. [8] A. Gupta, A. Mehra, and D. Bhatia, Approximate convexity in vector optimization, Bull. Aust. Math. Soc. 74 (2006), 207–218. [9] V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators, J. Optim. Theory Appl. 101 (1999), no. 3, 599–621. [10] B.C. Joshi, On generalized approximate convex functions and variational inequalities, RAIRO-Oper. Res. 55 (2021), S2999–S3008. [11] F.A. Khan, R.K. Bhardwaj, T. Ram, and M.A.S. Tom, On approximate vector variational inequalities and vector optimization problem using convexificator, AIMS Math. 7 (2022), no. 10, 18870–18882. [12] V. Laha and S.K. Mishra, On vector optimization problems and vector variational inequalities using convexifactors, J. Math. Programm. Oper. Res. 66 (2017), 1837–1850. [13] K.K. Lai, S.K. Mishra, M. Hassan, J. Bisht, and J.K. Maurya, Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators, J. Inequal. Appl. 2022 (2022), no. 1, 128. [14] X.F. Li and J.Z. Zhang, Necessary optimality conditions in terms of convexificators in Lipschitz optimization, J. Optim. Theory Appl. 131 (2006), 429–452. [15] X.F. Li and J.Z. Zhang, Stronger Kuhn-Tucker type conditions in nonsmooth multiobjective optimization: locally Lipschitz case, J. Optim. Theory Appl. 127 (2005), 367–388. [16] X.J. Long and N.J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math. 18 (2014), 687–699. [17] D.V. Luu, Convexifcators and necessary conditions for efficiency, Optim. 63 (2013), 321–335. [18] D.V. Luu, Necessary and sufficient conditions for efficiency via convexificators, J. Optim Theory Appl. 160 (2014), 510–526. [19] S.K. Mishra and V. Laha, On approximately star-shaped functions and approximate vector variational inequalities, J. Optim. Theory Appl. 156 (2013), 278–293. [20] S. K. Mishra and V. Laha, On Minty variational principle for nonsmooth vector optimization problems with approximate convexity, Optim. Lett. 10 (2016), 577–589. [21] S.K. Mishra and B.B. Upadhyay, Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency, Positivity 17 (2013), 1071–1083. [22] B.B. Upadhyay, P. Mishra, R.N. Mohapatra, and S. K. Mishra, On relationships between vector variational inequality and nonsmooth vector optimization problems via strict minimizers, Adv. Nonlinear Var. Inequal. 20 (2017), Paper No. 2. [23] B.B. Upadhyay, P. Mishra, R.N. Mohapatra, and S.K. Mishra, On the applications of nonsmooth vector optimization problems to solve generalized vector variational inequalities using convexificators, Adv. Intel. Syst. Comput. 991 (2020), 660–671. [24] Z. Wang, R. Li and G. Yu, Vector critical points and generalized quasi efficient solutions in nonsmooth multiobjective programming, J. Inequal. Appl. 2008 (2008), no. 1, 184. [25] X.Q. Yang and X.Y. Zheng, Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces, J. Global Optim. 40 (2008), 455–462. | ||
|
آمار تعداد مشاهده مقاله: 19,403 تعداد دریافت فایل اصل مقاله: 12,967 |
||