0
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Second-order necessary and sufficient optimality conditions for multiobjective interval-valued nonlinear programming

Received 23 Aug 2023, Accepted 10 Jul 2024, Published online: 21 Jul 2024

References

  • Osuna-Gómez R, Hernádez-Jiménez B, Chalco-Cano Y, et al. New efficiency conditions for multiobjective interval-valued programming problems. Inform Sci. 2017;420:235–248. doi: 10.1016/j.ins.2017.08.022
  • Antczak T. Saddle point criteria and Wolfe duality for convex nonsmooth interval-valued vector optimization problems. Pacific J Optim. 2020;16:1–18.
  • Chalco-Cano Y, Lodwick WA, Rufián-Lizana A. Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optim Decis Mak. 2013;12:305–322. doi: 10.1007/s10700-013-9156-y
  • Hung NH, Tuan HN, Tuyen NV. On approximate quasi Pareto solutions in nonsmooth semi-infinite interval-valued vector optimization problems. Appl Anal. 2023;102:2432–2448. doi: 10.1080/00036811.2022.2027385
  • Stefanini L, Arana-Jiménez M. Karush–Kuhn–Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability. Fuzzy Sets Syst. 2019;362:1–34. doi: 10.1016/j.fss.2018.04.009
  • Tung LT. Karush–Kuhn–Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions. J Appl Math Comput. 2020;62:67–91. doi: 10.1007/s12190-019-01274-x
  • Wu HC. On interval-valued nonlinear programming problems. J Math Anal Appl. 2008;338:299–316. doi: 10.1016/j.jmaa.2007.05.023
  • Wu HC. The Karush–Kuhn–Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions. European J Oper Res. 2009;196:49–60. doi: 10.1016/j.ejor.2008.03.012
  • Zhang J, Liu S, Li L, et al. The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optim Lett. 2014;8:607–631. doi: 10.1007/s11590-012-0601-6
  • Ahmad I, Singh D, Dar BA. Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative. Filomat. 2016;30:2121–2138. doi: 10.2298/FIL1608121A
  • Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming, theory and algorithms. New Jersey: Wiley-Interscience; 2006.
  • Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York: Springer; 2013.
  • Mordukhovich BS. Variational analysis and applications. Cham: Springer; 2018.
  • Andreani R, Behling R, Haeser G, et al. On second-order optimality conditions in nonlinear optimization. Optim Methods Softw. 2017;32:22–38. doi: 10.1080/10556788.2016.1188926
  • Cambini A, Martein L, Vlach M. Second order tangent sets and optimality conditions. Math Japon. 1999;49:451–461.
  • 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
  • Kawasaki H. An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems. Math Program. 1988;41:73–96. doi: 10.1007/BF01580754
  • Penot JP. Second-order conditions for optimization problems with constraints. SIAM J Control Optim. 1999;37:303–318. doi: 10.1137/S0363012996311095
  • Wang S. Second-order necessary and sufficient conditions in multiobjective programming. Numer Funct Anal Optim. 1991;12:237–252. doi: 10.1080/01630569108816425
  • 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
  • Bigi G, Castellani M. Second order optimality conditions for differentiable multiobjective problems. RAIRO Oper Res. 2000;34:411–426. doi: 10.1051/ro:2000122
  • Guerraggio A, Luc DT. Optimality conditions for C1,1 constrained multiobjective problems. J Optim Theory Appl. 2003;116:117–129. doi: 10.1023/A:1022114319999
  • Jiménez B, Novo V. First and second order sufficient conditions for strict minimality in multiobjective programming. Numer Funct Anal Optim. 2002;23:303–322. doi: 10.1081/NFA-120006695
  • Jiménez B, Novo V. Optimality conditions in differentiable vector optimization via second-order tangent sets. Appl Math Optim. 2004;49:23–144.
  • Hachimi M, Aghezzaf B. 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
  • Huy NQ, Kim DS, Tuyen NV. New second-order Karush–Kuhn–Tucker optimality conditions for vector optimization. Appl Math Optim. 2019;79:279–307. doi: 10.1007/s00245-017-9432-2
  • Tuyen NV, Huy NQ, Kim DS. Strong second-order Karush–Kuhn–Tucker optimality conditions for vector optimization. Appl Anal. 2020;99:103–120. doi: 10.1080/00036811.2018.1489956
  • Feng M, Li S. On second-order optimality conditions for continuously Fréchet differentiable vector optimization problems. Optimization. 2018;12:2117–2137. doi: 10.1080/02331934.2018.1545122
  • Wang J, Li S, Feng M. New second-order necessary optimality conditions for constrained vector optimization problems. Appl Anal. 2023;102:4886–4898. doi: 10.1080/00036811.2022.2147065
  • Goberna MA, Lopéz MA. Linear semi-infinite optimization. Chichester: Wiley; 1998.
  • Gutiérrez C, Jiménez B, Novo V. On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming. Math Program. 2010;123:199–223. doi: 10.1007/s10107-009-0318-1
  • Khanh PQ, Tuan ND. Second-order optimality conditions with the envelope-like effect in nonsmooth multiobjective mathematical programming II: optimality conditions. J Math Anal Appl. 2013;403:703–714. doi: 10.1016/j.jmaa.2012.12.075
  • Antczak T. On first and second order multiobjective programming with interval-valued objective functions. Appl Anal. 2024;103:1098–1117. doi:10.1080/00036811.2023.2232795.
  • Aubin JP, Frankowska H. Set-valued analysis. Boston, MA: Birkhäuser; 1990.
  • Mangasarian OL. Nonlinear programming. New York: McGraw Hill; 1969.
  • Alefeld G, Herzberger J. Introduction to interval computation. New York: Academic Press; 1983.
  • Minchenko L, Stakhovski S. On relaxed constant rank regularity condition in mathematical programming. Optimization. 2011;60:429–440. doi: 10.1080/02331930902971377
  • Guo L, Zhang J, Lin GH. New results on constraint qualifications for nonlinear extremum problems and extensions. J Optim Theory Appl. 2014;163:737–754. doi: 10.1007/s10957-013-0510-6
  • Kruger AY, Minchenk L, Outrata JV. On relaxing the Mangasarian–Fromovitz constraint qualification. Positivity. 2014;18:171–189. doi: 10.1007/s11117-013-0238-4
  • Khan AA, Tammer C, Zalinescu C. Set-valued optimization. Berlin: Springer; 2016.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.