پیوندهای مفید
آمار
| تعداد نشریات | 27 |
| تعداد شماره‌ها | 366 |
| تعداد مقالات | 3,243 |
| تعداد مشاهده مقاله | 4,754,606 |
| تعداد دریافت فایل اصل مقاله | 3,245,240 |
On well-posedness of generalized equilibrium problems involving -monotone bifunction | ||
| Journal of Hyperstructures | ||
| دوره 5، شماره 2، اسفند 2016، صفحه 151-168 اصل مقاله (342.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2016.2676 | ||
| نویسندگان | ||
| AYED HASHOOSH* 1؛ M. Alimohammady2 | ||
| 1Department of Mathematics, University of Mazandaran, Babolsar, Iran | ||
| 2Department of Mathematics, University of Mazandaran, P.O.Box 47416-1468, Babolsar, Iran | ||
| چکیده | ||
| The aim of this paper is to establish some uniqueness and well-posedness results for a general inequality of equilibrium problems type involving -monotone bifunction, whose solution is sought in a subset K of a Banach space X. Some metric character- izations and sucient conditions for these types of well-posedness are obtained. Moreover, we prove that the well-posedness of gen- eralized equilibrium problems is equivalent to the existence and uniqueness of its solution. | ||
| کلیدواژه‌ها | ||
| Equilibrium problems؛ Well-posed optimization problems؛ Monotonicity؛ Metric characterizations | ||
| مراجع | ||
|
[1] L. Q. Anh, P. Q. Khanh, and D. T. M. Van, Well-posedness under relaxed semi-continuity for bilevel equilibrium and optimization problems with equilibrium con-straints, Journal of Optimization Theory and Applications, 153 (2012) 42–59. [2] E. Bednarczuk and J. P. Penot, Metrically well-set minimization problems, Appl.Math. Optim. 26 (1992) 273–285. [3] M.Bianchi, G.Kassay and R.Pini, Well-posedness for vector equilibrium problems Math. Methods Oper. Res. 70 (2009) 171–182. [4] M. Bianchi, R. Pini, Sensitivity for parametric vector equilibria, Optimization 55 (2006) 221–230. [5] J. W. Chen, Y. J. Cho and X. Q. Ou, Levitin-polyakwell-posedness for set-valued optimization problems with constraints, Filomat, 28 (2014) 1345–1352. [6] J. W. Chen, Y. J. Cho and Z. P. Wang, The existence of solutions and well-posedness for bilevel mixed equilibrium problems in Banach spaces Taiwan. J. Math., 17 (2013) 725–748. [7] J. W. Chen, Z. P. Wang and L. Y. Yuan, Existence of solutions and α-well-posedness for a system of constrained set-valued variational inequalities, Numer. Algebra Control Optim., 3 (2013) 567–581. [8] J.W. Chen, Z. P.Wang and Y. J. Cho, Levitin-Polyak well-posedness by perturba-tions for systems of set-valued vector quasi-equilibrium problems, Math. Methods Oper. Res., 77 (2013), 33–64. [9] A. L. Dontchev and T. Zolezzi Well-Posed Optimization Problems. Springer-Verlag. Berlin (1993). [10] Y. P. Fang, N. J. Huang, and J. C. Yao, Well-posedness of mixed variational inequalities, inclusionproblems and fixed point problems, Journal of Global Opti-mization, 41 (2008)117–133. [11] Y. P Fang, R. Hu, and N. J. Huang, Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints. Comput. Math. Appl. 55 (2008) 89–100. [12] N. Hadjisavvas and H. Khatibzadeh, Maximal monotonicity of bifunctions, opti-mization 59, (2010) 147–160. [13] A.E.Hashoosh, M.Alimohammady and M.K.Kalleji, Existence Results for Some Equilibrium Problems Involving α-Monotone Bifunction, International Journal of Mathematics and Mathematical Sciences, 2016 (2016) 1–5. [14] X. X. Huang, Extended and strongly extended well-posedness of set-valued opti-mization problems, Math. Methods Oper. Res. 53 (2001)101–116. [15] K. Kimura, Y. C., Liou, S. Y. Wu, and J. C. Yao, Well-posedness for parametric vector equilibrium with applications J. Ind. Manag. Optim. 4 (2008) 313–327. [16] K. Kuratowski, Topology, vols. 1–2, Academic Press, New York, NY, (1968). [17] E.S.Levitin and B.T.Polyak, Convergence of minimizing sequences in conditional extremum problems Soviet Math. Dokl. 7 (1966) 764–767. [18] M. B.Lignola and J.Morgan, Well-posedness for optimization problems with con-straints defined by variational inequalities having a unique solution, J. Global Optim. 16 (2000) 57–67. [19] M.B. Lignola, Well-posedness and L-well-posedness for quasivariational inequal-ities, J. Optim. Theory Appl. 128 (2006) 119–138. [20] X. Long, N. Huang and K. Teo, Levitin-Polyak well-posedness for equilibrium problems with functional constraintsJ. Inequal. Appl. 2008 Article ID 657329 (2008) 1–14. [21] N.K.Mahato and C.Nahak, Equilibrium problems with generalized relaxed mono-tonicities in Banach spaces, Opsearch, 51 (2014) 257–269. [22] M. Margiocco, F. Patrone and L. Pusillo, A new approach to Tikhonov well-posedness for Nash equilibria, Optimization 40 (1997) 385–400. [23] M. Margiocco, F. Patrone and L. Pusillo, On the Tikhonov well-posedness of concave games and Cournot oligopoly games, J. Optim. Theory Appl. 112 (2002) 361–379. [24] M. Margiocco, F. Patrone, L. Pusillo, Metric characterizations of Tikhonov well-posedness in value, J. Optim. Theory Appl. 100 (1999) 377–387. [25] J. Morgan, Approximations and well-posedness in multicriteria games, Ann. Oper. Res. 137 (2005) 257–268. [26] J. Peng, Y. Wang and S. Wu, Levitin-Polyak well-posedness of generalized vector equilibrium problems, Taiwan. J. Math. 15 (2011) 2311–2330. [27] J. Salamon, Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems J. Glob. Optim. 47 (2010) 173–183. [28] L. SJ L.MH, Levitin-Polyak well-posedness of vector equilibrium problems Math. Methods Oper. Res. 69 (2009) 125–140. [29] A. N. Tykhonov, On the stability of the functional optimization problem USSR J. Comput. Math. Math. Phys. 6 (1966) 631–634. [30] A.Zaslavski,Generic well-posedness for a class of equilibrium problems J.In-equal.Appl.2008,Article ID 581917(2008)1–9. [31] K. Zhang , Z. Quan HE, and D. Peng GAO, Extended well- posedness for quasi-variational inequality, 10 1–10 (2009). [32] Y. Zhanga and T. Chen, A note on well-posedness of Nash-type games problems with set payoff , J. Nonlinear Sci. Appl. 9 (2016) 486–492 . [33] T. Zolezzi, Extended well-posedness of optimization problems, J. Optim. Theory Appl. 91 (1996) 257–266. [34] T.Zolezzi, Well-posedness criteria in optimization with application to the calculus of variations, Nonlinear Anal. TMA 25 (1995) 437–453. | ||
|
آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 63 |
||