Free Access
RAIRO-Oper. Res.
Volume 55, Number 2, March-April 2021
Page(s) 841 - 860
Published online 16 April 2021
  • N.L.H. Anh, Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18 (2014) 449–473. [Google Scholar]
  • J.P. Aubin, Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions, Mathematical Analysis and Applications, Part A, edited by L. Nachbin. Academic Press, New York (1981) 160–229. [Google Scholar]
  • J.P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhauser, Boston (1990). [Google Scholar]
  • H.P. Benson, An improved definition of proper efficiency for vector minimization with respect to cones. J. Math. Anal. Appl. 71 (1979) 232–241. [Google Scholar]
  • J.M. Bonnisseau and B. Cornet, Existence of equilibria when firms follow bounded losses pricing rules. J. Math. Econ. 17 (1988) 119–147. [Google Scholar]
  • G.Y. Chen and J. Jahn, Optimality conditions for set-valued optimization problems. Math. Methods Oper. Res. 48 (1988) 187–200. [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]
  • R. Cominetti, Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Optim. 21 (1990) 265–287. [Google Scholar]
  • H.W. Corley, Optimality conditions for maximizations of set-valued functions. J. Optim. Theory App. 58 (1988) 1–10. [Google Scholar]
  • A.L. Dontchev and R.T. Rockafellar, Implicit Functions and Solution Mappings. Springer, Berlin (2009). [CrossRef] [Google Scholar]
  • M. Durea, Optimality conditions for weak and firm efficiency in set-valued optimization. J. Math. Anal. Appl. 344 (2008) 1018–1028. [Google Scholar]
  • A. Götz and J. Jahn, The Lagrange multiplier rule in set-valued optimization. SIAM J. Optim. 10 (1999) 331–344. [Google Scholar]
  • C. Gutiérrez, B. Jiménez and V. Novo, On second order Fritz John type optimality conditions in nonsmooth multiobjective programming. Math. Program. Ser. B. 123 (2010) 199–223. [Google Scholar]
  • M.I. Henig, Proper efficiency with respect to cones. J. Optim. Theory App. 36 (1982) 387–407. [Google Scholar]
  • G. Isac and A.A. Khan, Dubovitskii-Milyutin approach in set-valued optimization. SIAM J. Control Optim. 47 (2008) 144–162. [Google Scholar]
  • J. Jahn, Vector Optimization: Theory, Applications, and Extensions. Springer, Berlin (2004). [Google Scholar]
  • J. Jahn and A.A. Khan, Generalized contingent epiderivatives in set-valued optimization: optimality conditions. Numer. Funct. Anal. Optim. 23 (2002) 807–831. [Google Scholar]
  • J. Jahn and R. Rauh, Contingent epiderivative 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 App. 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]
  • B. Jiménez and V. Novo, Optimality conditions in differentiable vector optimization via second-order tangent sets. Appl. Math. Optim. 49 (2004) 123–144. [Google Scholar]
  • A. Jofré and A. Jourani, Characterizations of the free disposal condition for nonconvex economies on infinite dimensional commodity spaces. SIAM J. Optim. 25 (2015) 699–712. [Google Scholar]
  • A. Jofré and J. Rivera, An intrinsic characterization of free disposal hypothesis. Econ. Lett. 92 (2006) 423–427. [Google Scholar]
  • H. Kawasaki, An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems. Math. Program. 41 (1988) 73–96. [CrossRef] [Google Scholar]
  • A.A. Khan and C. Tammer, Second-order optimality conditions in set-valued optimization via asymptotic derivatives. optimization 62 (2013) 743–758. [Google Scholar]
  • P.Q. Khanh and N.D. Tuan, Second order optimality conditions with the envelope-like effect in nonsmooth multiobjective programming II: optimality conditions. J. Math. Anal. Appl. 403 (2013) 703–714. [Google Scholar]
  • P.Q. Khanh and N.D. Tuan, Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions. Nonlinear Anal. 77 (2013) 130–148. [Google Scholar]
  • P.Q. Khanh and N.M. Tung, Second-order optimality conditions with the envelope-like effect for set-valued optimization. J. Optim. Theory App. 167 (2015) 68–90. [Google Scholar]
  • P.Q. Khanh and N.M. Tung, Existence and boundedness of second-order Karush–Kuhn–Tucker multipliers for set-vlued optimization with variable ordering structures. Taiwan. J. Math. 22 (2018) 1001–1029. [Google Scholar]
  • P.Q. Khanh and N.M. Tung, Higher-order Karush–Kuhn–Tucker conditions in nonsmooth optimization. SIAM J. Optim. 28 (2018) 820–848. [Google Scholar]
  • S.J. Li, K.L. Teo and X.Q. Yang, Higher-order Mond-Weir duality for set-valued optimization. J. Comput. Appl. Math. 217 (2008) 339–349. [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 App. 152 (2012) 587–604. [Google Scholar]
  • D.T. Luc, Theory of Vector Optimization. Springer, Berlin (1989). [Google Scholar]
  • B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, Vol. I Basic Theory, Vol. II Applications. Springer, Berlin (2006). [Google Scholar]
  • J.P. Penot, Second order conditions for optimization problems with constraints. SIAM J. Control Optim. 37 (1999) 303–318. [Google Scholar]
  • S.M. Robinson, Regularity and stability for convex multivalued functions. Math. Oper. Res. 1 (1976) 130–143. [Google Scholar]
  • P.H. Sach, N.D. Yen and B.D. Craven, Generalized invexity and duality theorems with multifunctions. Numer. Funct. Anal. Optim. 15 (1994) 131–153. [Google Scholar]
  • X.K. Sun and S.J. Li, Lower Studniarski derivative of the perturbation map in parametrized vector optimization. Optim Lett. 5 (2011) 601–614. [Google Scholar]
  • X.K. Sun and S.J. Li, Generalized second-order contingent epiderivatives in parametric vector optimization problems. J. Global Optim. 58 (2014) 351–363. [Google Scholar]
  • X.K. Sun, Z.Y. Peng and X.L. Guo, Some characterizations of robust optimal solutions for uncertain convex optimization problems. Optim Lett. 10 (2016) 1463–1478. [Google Scholar]
  • X.K. Sun, K.L. Teo and L.P. Tang, Dual approaches to characterize robust optimal solution sets for a class of uncertain optimization problems. J. Optim. Theory App. 182 (2019) 984–1000. [Google Scholar]
  • X.K. Sun, K.L. Teo, J. Zeng and L.Y. Liu, Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty. Optimization 69 (2020) 2109–2129. [Google Scholar]
  • C. Ursescu, Multifunctions with closed convex graph. Czech. Math. J. 25 (1975) 438–441. [Google Scholar]
  • T. Weir and B. Mond, Generalized convexity and duality in multiple objective programming. Bull. Aust. Math. Soc. 39 (1989) 287–299. [Google Scholar]
  • X.Y. Zheng and K.F. Ng, The Fermat rule for multifunctions on Banach spaces. Math. Program. Ser. A 104 (2005) 69–90. [Google Scholar]
  • S.K. Zhu, S.J. Li and K.L. Teo, Second-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization. J. Global Optim. 58 (2014) 673–679. [Google Scholar]
  • J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 (1979) 49–62. [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.