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Applicable Analysis
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Volume 99, 2020 - Issue 1
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Articles

Strong second-order Karush–Kuhn–Tucker optimality conditions for vector optimization

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Pages 103-120 | Received 23 May 2017, Accepted 11 Jun 2018, Published online: 26 Jun 2018

References

  • Hiriart-Urruty JB, Strodiot JJ, Nguyen VH. Generalized Hessian matrix and second-order optimality conditions for problems with C1,1 data. Appl Math Optim. 1984;11:43–56. doi: 10.1007/BF01442169
  • Jahn J. Vector optimization. New York (NY): Springer; 2004.
  • Burachik RS, Rizvi MM. On weak and strong Kuhn-Tucker conditions for smooth multiobjective optimization. J Optim Theory Appl. 2012;155:477–491. doi: 10.1007/s10957-012-0078-6
  • Maeda T. Constraint qualification in multiobjective optimization problems: differentiable case. J Optim Theory Appl. 1994;80:483–500. doi: 10.1007/BF02207776
  • Preda V, Chiţescu I. On constraint qualification in multiobjective optimization problems: semidifferentiable case. J Optim Theory Appl. 1999;100:417–433. doi: 10.1023/A:1021794505701
  • Giorgi G, Jiménez B, Novo V. Strong Kuhn-Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problem. Top. 2009;17:288–304. doi: 10.1007/s11750-008-0058-z
  • Golestani M, Nobakhtian S. Nonsmooth multiobjective programming: strong KuhnTucker conditions. Positivity. 2013;17:711–732. doi: 10.1007/s11117-012-0201-9
  • Chuong TD, Yao JC. Isolated and proper efficiencies in semi-infinite vector optimization problems. J Optim Theory Appl. 2014;162:447–462. doi: 10.1007/s10957-013-0425-2
  • Wang S. Second order necessary and sufficient conditions in multiobjective programming. Numer Funct Anal Optim. 1991;12:237–252. doi: 10.1080/01630569108816425
  • Bigi G, Castellani M. Second order optimality conditions for differentiable multiobjective problems. RAIRO Oper Res. 2000;34:411–426. doi: 10.1051/ro:2000122
  • Bigi G, Castellani M. Uniqueness of KKT multipliers in multiobjective optimization. Appl Math Lett. 2004;17:1285–1290. doi: 10.1016/j.aml.2003.10.011
  • Aghezzaf B, Hachimi M. Second-order optimality conditions in multiobjective optimization problems. J Optim Theory Appl. 1999;102:37–50. doi: 10.1023/A:1021834210437
  • Aghezzaf B, Hachimi M. New results on second-order optimality conditions in vector optimization problems. J Optim Theory Appl. 2007;135:117–133. doi: 10.1007/s10957-007-9242-9
  • Guerraggio A, Luc DT, Minh NB. Second-order optimality conditions for C1 multiobjective programming problems. Acta Math Vietnam. 2001;26:257–268.
  • Khanh PQ, Tung NM. Second-order conditions for open-cone minimizers and firm minimizers in set-valued optimization subject to mixed constraints. J Optim Theory Appl. 2016;171:45–69. doi: 10.1007/s10957-016-0995-x
  • Jiménez B, Novo V. Second order necessary conditions in set constrained differentiable vector optimization. Math Methods Oper Res. 2003;58:299–317. doi: 10.1007/s001860300283
  • Gutiérrez C, Jiménez B, Novo V. New second-order directional derivative and optimality conditions in scalar and vector optimization. J Optim Theory Appl. 2009;142:85–106. doi: 10.1007/s10957-009-9525-4
  • Tuan ND. First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives. Appl Math Comput. 2015;251:300–317.
  • Tuan ND. On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions. Appl Math Optim. 2016;77:515–539. doi: 10.1007/s00245-016-9383-z
  • Maeda T. Second-order conditions for efficiency in nonsmooth multiobjective optimization. J Optim Theory Appl. 2004;122:521–538. doi: 10.1023/B:JOTA.0000042594.46637.b4
  • Kim DS, Tuyen NV. A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems. RAIRO Oper Res. 2017. DOI:10.1051/ro/2017026.
  • Rizvi MM, Nasser M. New second-order optimality conditions in multiobjective optimization problems: differentiable case. J Indian Inst Sci. 2006;86:279–286.
  • Huy NQ, Tuyen NV. New second-order optimality conditions for a class of differentiable optimization problems. J Optim Theory Appl. 2016;171:27–44. doi: 10.1007/s10957-016-0980-4
  • Mordukhovich BS. Variational analysis and generalized differentiation, I: basic theory, Grundlehren series (fundamental principles of mathematical sciences). Vol. 330. Berlin: Springer; 2006.
  • Clarke FH. Optimization and nonsmooth analysis. Philadelphia (PA): SIAM; 1990.
  • Kuhn HW, Tucker AW. Nonlinear programming. In: Neyman J, editor. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability; 1950 Jul 31–Aug 12; Berkeley (CA): University of California press; 1951. p. 481–492.
  • Geoffrion AM. Proper efficiency and the theory of vector maximization. J Math Anal Appl. 1968;22:618–630. doi: 10.1016/0022-247X(68)90201-1
  • Mangasarian OL. Nonlinear programming. New York (NY): McGraw-Hill; 1969.
  • Borwein JM, Fitzpatrick S. Characterization of Clarke subgradients among one-dimensional multifunctions. In: Glover BM, Jeyakumar V, editors. Proceedings of the optimization miniconference II; 1994 Jul 14; Sydney (NSW): University of New South Wales; 1995. p. 61–64.

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