On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

Open Access

Issue		RAIRO-Oper. Res. Volume 56, Number 3, May-June 2022


Page(s)		1373 - 1395
DOI		https://doi.org/10.1051/ro/2022062
Published online		02 June 2022

N.L.H. Anh, Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives. Positivity 21 (2017) 255–272. [CrossRef] [MathSciNet] [Google Scholar]
N.L.H. Anh, Some results on sensitivity analysis in set-valued optimization. Positivity 21 (2017) 1527–1543. [CrossRef] [MathSciNet] [Google Scholar]
N.L.H. Anh, Second-order composed contingent derivatives of perturbation maps in set-valued optimization. Comput. Appl. Math. 38 (2019) 145. [CrossRef] [Google Scholar]
N.L.H. Anh and P.Q. Khanh, Variational sets of perturbation maps and applications to sensitivity analysis for constrained vector optimization. J. Optim. Theory Appl. 158 (2013) 363–384. [Google Scholar]
J.P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhauser, Boston (1990). [Google Scholar]
J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, New York (2000). [Google Scholar]
T.D. Chuong, Clarke coderivatives of efficient point multifunctions in parametric vector optimization. Nonlinear Anal. 74 (2011) 273–285. [CrossRef] [MathSciNet] [Google Scholar]
T.D. Chuong, Derivatives of the efficient point multifunction in parametric vector optimization problems. J. Optim. Theory Appl. 156 (2013) 247–265. [Google Scholar]
T.D. Chuong, Normal subdifferentials of effcient point multifunctions in parametric vector optimization. Optim. Lett. 7 (2013) 1087–1117. [CrossRef] [MathSciNet] [Google Scholar]
T.D. Chuong and J.-C. Yao, Coderivatives of efficient point multifunctions in parametric vector optimization. Taiwan. J. Math. 13 (2009) 1671–1693. [MathSciNet] [Google Scholar]
T.D. Chuong and J.-C. Yao, Generalized clarke epiderivatives of parametric vector optimization problems. J. Optim. Theory Appl. 147 (2010) 77–94. [CrossRef] [MathSciNet] [Google Scholar]
T.D. Chuong and J.-C. Yao, Fréchet subdifferentials of efficient point multifunctions in parametric vector optimization. J. Global Optim. 57 (2013) 1229–1243. [CrossRef] [MathSciNet] [Google Scholar]
H.T.H. Diem, P.Q. Khanh and L.T. Tung, On higher-order sensitivity analysis in nonsmooth vector optimization. J. Optim. Theory Appl. 162 (2014) 463–488. [Google Scholar]
N.Q. Huy and G.M. Lee, On sensitivity analysis in vector optimization. Taiwan. J. Math. 11 (2007) 945–958. [Google Scholar]
N.Q. Huy and G.M. Lee, Sensitivity of solutions to a parametric generalized equation. Set-Valued Anal. 16 (2008) 805–820. [CrossRef] [MathSciNet] [Google Scholar]
A. Khan, C. Tammer and C. Zălinescu, Set-Valued Optimization – An Introduction with Applications. Springer, Berlin (2015). [Google Scholar]
H. Kuk, T. Tanino and M. Tanaka, Sensitivity analysis in parametrized convex vector optimization. J. Math. Anal. Appl. 202 (1996) 511–522. [CrossRef] [MathSciNet] [Google Scholar]
G.M. Lee and N.Q. Huy, On proto-differentiability of generalized perturbation maps. J. Math. Anal. Appl. 324 (2006) 1297–1309. [CrossRef] [MathSciNet] [Google Scholar]
A.B. Levy and R.T. Rockafellar, Sensitivity analysis of solutions to generalized equations. Trans. Am. Math. Soc. 345 (1994) 661–671. [CrossRef] [Google Scholar]
S.J. Li and C.M. Liao, Second-order differentiability of generalized perturbation maps. J. Global Optim. 52 (2012) 243–252. [CrossRef] [MathSciNet] [Google Scholar]
S.J. Li, X.K. Sun and J. Zhai, Second-order contingent derivatives of set-valued mappings with application to set-valued optimization. Appl. Math. Comput. 218 (2012) 6874–6886. [MathSciNet] [Google Scholar]
D.T. Luc, M. Soleimani-damaneh and M. Zamani, Semi-differentiability of the marginal mapping in vector optimization. SIAM J. Optim. 28 (2018) 1255–1281. [CrossRef] [MathSciNet] [Google Scholar]
B.S. Mordukhovich, Variational Analysis and Generalized Differentiation. I: Basic Theory. Springer, Berlin (2006). [Google Scholar]
B.S. Mordukhovich, Variational Analysis and Generalized Differentiation. II: Applications. Springer, Berlin (2006). [Google Scholar]
Z. Peng and Z. Wan, Second-order composed contingent derivative of the perturbation map in multiobjective optimization. Asia Pac. J. Oper. Res. 37 (2020) 2050002. [CrossRef] [MathSciNet] [Google Scholar]
R.T. Rockafellar, Proto-differentiablility of set-valued mappings and its applications in optimization. Ann. Inst. Non Linéaire. H. Poincaré Anal. 6 (1989) 449–482. [CrossRef] [Google Scholar]
D.S. Shi, Contingent derivative of the perturbation map in multiobjective optimization. J. Optim. Theory Appl. 70 (1991) 385–396. [Google Scholar]
D.S. Shi, Sensitivity analysis in convex vector optimization. J. Optim. Theory Appl. 77 (1993) 145–159. [Google Scholar]
X.K. Sun and S.J. Li, Generalized second-order contingent epiderivatives in parametric vector optimization problem. J. Glob. Optim. 58 (2014) 351–363. [CrossRef] [Google Scholar]
T. Tanino, Sensitivity analysis in multiobjective optimization. J. Optim. Theory Appl. 56 (1988) 479–499. [Google Scholar]
T. Tanino, Stability and sensitivity analysis in convex vector optimization. SIAM J. Control Optim. 26 (1988) 521–536. [CrossRef] [MathSciNet] [Google Scholar]
L.T. Tung, Second-order radial-asymptotic derivatives and applications in set-valued vector optimization. Pac. J. Optim. 13 (2017) 137–153. [MathSciNet] [Google Scholar]
L.T. Tung, Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization. Positivity 21 (2017) 1647–1673. [CrossRef] [MathSciNet] [Google Scholar]
L.T. Tung, On second-order proto-differentiability of perturbation maps. Set-Valued Var. Anal. 26 (2018) 561–579. [CrossRef] [MathSciNet] [Google Scholar]
L.T. Tung, On higher-order proto-differentiability of perturbation maps. Positivity 24 (2020) 441–462. [CrossRef] [MathSciNet] [Google Scholar]
L.T. Tung, On higher-order proto-differentiability and higher-order asymptotic proto-differentiability of weak perturbation maps in parametric vector optimization. Positivity 25 (2021) 579–604. [CrossRef] [MathSciNet] [Google Scholar]
L.T. Tung, On second-order composed proto-differentiability of proper perturbation maps in parametric vector optimization problems. Asia Pac. J. Oper. Res. 38 (2021) 2050040. [CrossRef] [Google Scholar]
L.T. Tung and P.T. Hung, Sensitivity analysis in parametric vector optimization in Banach spaces via τ^w-contingent derivatives. Turk. J. Math. 44 (2020) 152–168. [CrossRef] [MathSciNet] [Google Scholar]
Q.L. Wang and S.J. Li, Second-order contingent derivative of the pertubation map in multiobjective optimization. Fixed Point Theory Appl. 2011 (2011) 1–13. [Google Scholar]
Q.L. Wang and S.J. Li, Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization. Optim. Lett. 6 (2012) 731–748. [CrossRef] [MathSciNet] [Google Scholar]
Q.L. Wang and X.Y. Zhang, Second-order composed radial derivatives of the Benson proper perturbation map for parametric multi-objective optimization problems. Asia Pac. J. Oper. Res. 37 (2020) 2040011. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.