Xu, Yihong; Li, Min; Peng, Zhenhua A note on “Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality”. (English) Zbl 1343.32007 Positivity 20, No. 2, 295-298 (2016). Summary: The note points out that the sufficiency of proposition 2.1 in [N. Le H. Anh, ibid. 18, No. 3, 449–473 (2014; Zbl 1298.49023)] is erroneous and we provide an example to illustrate it. Also the proof of proposition 2.2 in [loc. cit.] is incorrect and we give a new proof. Cited in 1 Document MSC: 32F17 Other notions of convexity in relation to several complex variables 46G05 Derivatives of functions in infinite-dimensional spaces 90C29 Multi-objective and goal programming 90C46 Optimality conditions and duality in mathematical programming Keywords:generalized subconvexlike; convex cone; set-valued map Citations:Zbl 1298.49023 PDFBibTeX XMLCite \textit{Y. Xu} et al., Positivity 20, No. 2, 295--298 (2016; Zbl 1343.32007) Full Text: DOI References: [1] Yang, X.M., Yang, X.Q., Chen, G.Y.: Theorems of the alternative and optimization with set-valued maps. J. Optim. Theory Appl. 107, 627-640 (2000) · Zbl 0966.90071 · doi:10.1023/A:1026407517917 [2] Yang, X.M., Li, D., Wang, S.Y.: Near-subconvexlikeness in vector optimization with set-valued functions. J.Optim. Theory Appl. 110, 413-427 (2001) · Zbl 1012.90061 · doi:10.1023/A:1017535631418 [3] Sach, P.H.: New generalized convexity notion for set-valued maps and application to vector optimization. J. Optim. Theory Appl. 125, 157-179 (2005) · Zbl 1090.90174 · doi:10.1007/s10957-004-1716-4 [4] Xu, Yihong: Song, Xiaoshuai: Relationship between ic-cone-convexness and nearly cone-subconvexlikeness. Appl. Math. Lett. 24, 1622-1624 (2011) · Zbl 1218.52003 · doi:10.1016/j.aml.2011.04.018 [5] Anh, N.L.H.: Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18, 449-473 (2014) · Zbl 1298.49023 · doi:10.1007/s11117-013-0254-4 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.