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Date Published: 25/04/2018
Online Published: 25/04/2018
Abstract Views: 27
Views PDF: 46
DOI: https://doi.org/10.52714/dthu.31.4.2018.570
Issue
No. 31 (2018): Part B - Natural Sciences
Section
Natural Sciences Issue
How to Cite
Dang, T. B. V., & Vo, D. T. (2018). Generalized Studniarski derivatives and its applications. Dong Thap University Journal of Science, 31, 60-64. https://doi.org/10.52714/dthu.31.4.2018.570

Generalized Studniarski derivatives and its applications

Thi Bich Van Dang, Duc Thinh Vo1
1 Dong Thap University

Main Article Content

Abstract

 In this paper, we introduce and state some properties of generalized Studniarski derivatives. Then, we present some applications of these derivatives in studying the stability of multi-valued maps and optimality conditions.

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Generalized Studniarski derivative, optimality conditions, stability

References

[1]. N. L. H. Anh (2014), “Higher-order optimality conditions in set–valued optimization using Studniarski derivatives and applications to duality”, Positivity, (18), p. 449-473.
[2]. N. L. H. Anh and P. Q. Khanh and L. T. Tung (2011), Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization, Nonlinear Anal, (74), p. 7365-7379.
[3]. N. L. H. Anh (2016), Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives, Positivity, (21), p. 255-272.
[4]. J. F. Bonnans and A. Shapiro (2000), Perturbation analysis of optimization problems, Springer-Verlag, New York.
[5]. B. Jiménez and V. Novo (2003), “Second-order necessary conditions in set constrained differentiable vecter optimization”, Math. Methods Oper. Res, (58), p. 299-317.
[6]. P. Q. Khanh and N. D. Tuan (2008), “Variational sets of multivalued mappings and a unified study of optimality conditions”, J. Optim. Theory Appl, (139), p. 45-67.
[7]. D. V. Luu, (2008), “Higher-order necessary and sufficient conditions for strict local Pareto minima in tems of Studniarski’s derivaties”, Optimization, (57), p. 593-605.
[8]. B. S. Mordukhovich (2005), Variational analysis and generalized differentiation I, Springer, Berlin.
[9]. B. S. Mordukhovich, N. M. Nam (2014), An easy path to convex analysis and applications, Morgan & Claypool Publishers, Willistion.
[10]. M. Studniarski (1986), “Necessary and sufficient conditions for isolated local minima of nonsmooth functions”, SIAM J. Control Optim, (24), p. 1044-1049.
[11]. X. K. Sun and S. J. Li (2011), “Lower Studniarski derivative of the perturbation map in parametrized vertor optimization”, Optim. Lett, (5), p. 601-614.

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