Free Access
Issue
RAIRO-Oper. Res.
Volume 54, Number 4, July-August 2020
Page(s) 949 - 959
DOI https://doi.org/10.1051/ro/2019033
Published online 16 April 2020
  • N.L.H. Anh, Mixed type duality for set-valued optimization problems via higher-order radial epiderivatives. Numer. Funct. Anal. Optim. 37 (2016) 823–838. [Google Scholar]
  • N.L.H. Anh, P.Q. Khanh and L.T. Tung, Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization. Nonlinear Anal. 74 (2011) 7365–7379. [CrossRef] [Google Scholar]
  • J.P. Aubin, Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclutions. In: Advances in Mathematics Supplementary Studies 7A, edited by L. Nachbin. Academic Press, New York (1981) 159–229. [Google Scholar]
  • J.P. Aubin and H. Frankowska, Set-valued Analysis. Birkhäuser, Boston, USA (1990). [Google Scholar]
  • E.M. Bednarczuk and W. Song, Contingent epiderivative and its applications to set-valued optimization. Control Cybernet. 27 (1998) 1–49. [Google Scholar]
  • H.P. Benson, An improved definition of proper efficiency for vector maximization with respect to cones. J. Math. Anal. Appl. 71 (1979) 232–241. [Google Scholar]
  • C.R. Chen, S.J. Li and K.L. Teo, Higher order weak epiderivatives and applications to duality and optimality conditions. Comput. Math. Appl. 57 (2009) 1389–1399. [Google Scholar]
  • G.Y. Chen and J. Jahn, Optimality conditions for set-valued optimization problems. Math. Methods Oper. Res. 48 (1998) 187–200. [CrossRef] [Google Scholar]
  • G.Y. Chen and W.D. Rong, Characterizations of the Benson proper efficiency for nonconvex vector optimization. J. Optim. Theory Appl. 98 (1998) 365–384. [Google Scholar]
  • H.W. Corley, Optimality condition for maximizations of set-valued functions. J. Optim. Theory Appl. 58 (1988) 1–10. [Google Scholar]
  • M. Durea, First and second order optimality conditions for set-valued optimization problems. Rend. Circ. Mat. Palermo. 2 (2004) 451–468. [CrossRef] [Google Scholar]
  • F. Flores-Bazán, Optimality conditions in nonconvex set-valued optimization. Math. Methods Oper. Res. 53 (2001) 403–417. [CrossRef] [Google Scholar]
  • J. Jahn, Vector Optimization Theory, Applications and Extensions. Springer, Berlin, USA (2004). [Google Scholar]
  • J. Jahn and R. Rauh, Contingent epiderivatives and set-valued optimization. Math. Methods Oper. Res. 46 (1997) 193–211. [CrossRef] [Google Scholar]
  • J. Jahn, A.A. Khan and P. Zeilinger, Second-order optimality conditions in set optimization. J. Optim. Theory Appl. 125 (2005) 331–347. [Google Scholar]
  • B. Jiménez and V. Novo, Second-order necessary conditions in set constrained differentiable vector optimization. Math. Methods Oper. Res. 58 (2003) 299–317. [CrossRef] [Google Scholar]
  • S.J. Li, K.L. Teo and X.Q. Yang, Higher-order optimality conditions for set-valued optimization. J. Optim. Theory Appl. 37 (2008) 533–553. [Google Scholar]
  • S.J. Li, S.K. Zhu and K.L. Teo, New generalized second-order contingent epiderivatives and set-valued optimization problems. J. Optim. Theory Appl. 152 (2012) 587–604. [Google Scholar]
  • Z. Li, A theorem of the alternative and its application to the optimization of set-valued maps. J. Optim. Theory Appl. 100 (1999) 365–375. [Google Scholar]
  • X.J. Long, J.W. Peng and M.M. Wong, Generalized radial epiderivatives and nonconvex set-valued optimization problems. Appl. Anal. 91 (2012) 1891–1900. [Google Scholar]
  • D.T. Luc, Theory of Vector Optimization. Springer, Berlin, USA (1989). [CrossRef] [Google Scholar]
  • Z.H. Peng and Y.H. Xu, New second-order tangent epiderivatives and applications to set-valued optimization. J. Optim. Theory Appl. 172 (2017) 128–140. [Google Scholar]
  • J.P. Penot, Second-order conditions for optimization problems with constraints. SIAM J. Control Optim. 37 (1998) 303–318. [Google Scholar]
  • B.H. Sheng and S.Y. Liu, On the generalized Fritz John optimality conditions of vector optimization with set-valued maps under Benson proper efficiency. Appl. Math. Mech. 23 (2002) 1444–1451. [Google Scholar]
  • J. Song and X.H. Gong, Approximation of the cone efficient solution for vector optimization problem. OR Trans. 11 (2007) 52–58. [Google Scholar]
  • A. Taa, Set-valued derivatives of multifunctions and optimality conditions. Numer. Funct. Anal. Optim. 19 (1998) 121–140. [Google Scholar]
  • Q.L. Wang, X.B. Li and G.L. Yu, Second-order weak composed epiderivatives and applications to optimality conditions. J. Ind. Manag. Optim. 9 (2013) 455–470. [Google Scholar]
  • Q.L. Wang and G.L. Yu, Higher-order weakly generalized epiderivatives and applications to optimality conditions. J. Appl. Math. 691018 (2012). [Google Scholar]

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