Zhang, W. Y. Well-posedness for convex symmetric vector quasi-equilibrium problems. (English) Zbl 1242.49054 J. Math. Anal. Appl. 387, No. 2, 909-915 (2012). Summary: In this paper, the notion of a generalized Levitin–Polyak well-posedness is defined for symmetric vector quasi-equilibrium problems. Sufficient conditions are given for the generalized Levitin–Polyak well-posedness. Moreover, it is shown that the results can be refined in the convex case. Cited in 1 ReviewCited in 10 Documents MSC: 49K40 Sensitivity, stability, well-posedness Keywords:symmetric vector quasi-equilibrium problems; generalized Levitin-Polyak well-posedness; convexity PDF BibTeX XML Cite \textit{W. Y. Zhang}, J. Math. Anal. Appl. 387, No. 2, 909--915 (2012; Zbl 1242.49054) Full Text: DOI References: [1] Tykhonov, A. N., On the stability of the functional optimization problem, USSR Comput. Math. Math. Phys., 6, 4, 28-33 (1966) [2] Levitin, E. S.; Polyak, B. T., Convergence of minimizing sequences in conditional extremum problems, Sov. Math. Dokl., 7, 764-767 (1966) · Zbl 0161.07002 [3] Konsulova, A. S.; Revalski, J. P., Constrained convex optimization problems well-posedness and stability, Numer. Funct. Anal. Optim., 15, 889-907 (1994) · Zbl 0830.90119 [4] Huang, X. X.; Yang, X. Q., Levitin-Polyak well-posedness of constrained vector optimization problems, J. Global Optim., 37, 287-304 (2007) · Zbl 1149.90133 [5] Huang, X. X.; Yang, X. Q., Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints, J. Ind. Manag. Optim., 3, 4, 671-684 (2007) · Zbl 1137.49025 [6] Li, S. J.; Li, M. H., Levitin-Polyak well-posedness of vector equilibrium problems, Math. Methods Oper. Res., 69, 125-140 (2009) · Zbl 1190.90266 [7] Fu, J. Y., Symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl., 285, 708-713 (2003) · Zbl 1031.49013 [8] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Student, 63, 123-145 (1994) · Zbl 0888.49007 [9] Chen, J. C.; Gong, X. H., The stability of set of solutions for symmetric vector quasi-equilibrium problems, J. Optim. Theory Appl., 136, 359-374 (2008) · Zbl 1145.90072 [10] Huang, X. X.; Yang, X. Q.; Zhu, D. L., Levitin-Polyak well-posedness of variational inequality problems with functional constraints, J. Global Optim., 44, 159-174 (2009) · Zbl 1191.90083 [12] Farajzadeh, Ali P., On the symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl., 322, 1099-1110 (2006) · Zbl 1130.49008 [13] Dontchev, A.; Zolezzi, T., Well-Posed Optimization Problems, Lecture Notes in Math., vol. 1543 (1993), Springer-Verlag: Springer-Verlag Berlin · Zbl 0797.49001 [14] Lucchetti, R., Convexity and Well-Posed Problems, CMS Books Math., vol. 22 (2006), Springer: Springer New York · Zbl 1106.49001 [15] Nieuwenhuis, J. W., Some minimax theorems in vector-valued functions, J. Optim. Theory Appl., 40, 463-475 (1983) · Zbl 0494.90073 [16] Rockafellar, R. T.; Wets, R. J.-B., Variational Analysis (1998), Springer-Verlag: Springer-Verlag Berlin · Zbl 0888.49001 [17] Lucchetti, R. E.; Miglierina, E., Stability for convex vector optimization problems, Optimization, 53, 5-6, 517-528 (2004) · Zbl 1153.90536 [18] Luc, D. T., Theory of Vector Optimization (1989), Springer-Verlag: Springer-Verlag Berlin [19] Aubin, J. P.; Frankowska, H., Set-Valued Analysis (1990), Birkhäuser: Birkhäuser Boston [20] Tanino, T., Stability and sensitivity analysis in convex vector optimization, SIAM J. Control Optim., 26, 521-536 (1988) · Zbl 0654.49011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.