Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications

References

• Aubin J-P, Frankowska H. Set-valued analysis. Boston: Birkhauser; 1990.
   Google Scholar
• Auslender A. Stability in mathematical programming with nondifferentiable data. SIAM J Cont Optim. 1984;22:239–254. doi: 10.1137/0322017
   Web of Science ®Google Scholar
• Constantin E. Higher order necessary conditions in smooth constrained optimization. Commun Math. 2009;479:41–49. doi: 10.1090/conm/479/09341
   Google Scholar
• Constantin E. Second-order optimality conditions for problems with locally Lipschitz data via tangential directions. Comm Appl Nonlinear Anal. 2011;18(2):75–84.
   Google Scholar
• Constantin E. Higher-order sufficient conditions for problems with Gâteaux differentiable data. Revue Roumaini de Mathématique Pures and Appliquées, Tome LXIV, 1; 2019.
   Google Scholar
• Gutiérrez C, Jiménez B, Novo V. On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming. Math Program. 2010;123(B):199–223. doi: 10.1007/s10107-009-0318-1
   Google Scholar
• Jiménez B, Novo V. A finite dimensional extension of Lyusternik theorem with applications to multiobjective optimization. Appl Math Optim. 2002;270:340–356.
   Google Scholar
• Lee H, Pavel N. Higher order optimality conditions and its applications. Pan American Math J. 2004;14:11–24.
   Google Scholar
• Luu DV. Higher-order optimality conditions in nonsmooth cone-constrained multiobjective programming. Nonlinear Funct Anal Appl. 2010;15:381–393.
   Google Scholar
• Luu DV. Second-order necessary efficiency conditions for nonsmooth vector equilibrium problems. J Global Optim. 2018;70:437–453. doi: 10.1007/s10898-017-0556-3
   Web of Science ®Google Scholar
• Studniarski M. Necessary and sufficient conditions for isolated local minima of nonsmooth functions. SIAM J Control Optim. 1986;24:1044–1049. doi: 10.1137/0324061
   Web of Science ®Google Scholar
• Taa A. Second order conditions for nonsmooth multiobjective optimization problems with inclusion constrains. J Global Optim. 2011;50:271–291. doi: 10.1007/s10898-010-9580-2
   Web of Science ®Google Scholar
• Ward DE. Characterizations of strict local minima and necessary conditions for weak sharp minia. J Optim Theory Appl. 1994;80:551–571. doi: 10.1007/BF02207780
   Web of Science ®Google Scholar
• Bonnans J-F, Cominetti R, Shapiro A. Second order optimality conditions based on parabolic second order tangent sets. SIAM J Optim. 1999;9(2):466–492. doi: 10.1137/S1052623496306760
   Web of Science ®Google Scholar
• Chuong TD. Optimality conditions for nonsmooth multiobjective bilevel optimization problems. Ann Oper Res. 2018. DOI:10.1007/s10479-017-2734-6
   PubMed Web of Science ®Google Scholar
• Daniele P. Lagrange multipliers and infinite-dimensional equilibrium problems. J Global Optim. 2008;40:65–70. doi: 10.1007/s10898-007-9182-9
   Web of Science ®Google Scholar
• Gong XH. Optimality conditions for vector equilibrium problems. J Math Anal Appl. 2008;342:1455–1466. doi: 10.1016/j.jmaa.2008.01.026
   Web of Science ®Google Scholar
• Gong XH. Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal. 2010;73:3598–3612. doi: 10.1016/j.na.2010.07.041
   Web of Science ®Google Scholar
• Long XJ, Huang YQ, Peng ZY. Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints. Optim Lett. 2011;5:717–728. doi: 10.1007/s11590-010-0241-7
   Web of Science ®Google Scholar
• Jiménez B, Novo V. Optimality conditions in directionally differentiable pareto problems with a set constraint via tangent sets. Numer Funct Anal Optim. 2003;24(5–6):557–574. doi: 10.1081/NFA-120023868
   Web of Science ®Google Scholar
• Luu DV. Higher-order necessary and sufficient conditions for strict local Pareto minima in terms of Studniarski's derivatives. Optimization. 2008;57:593–605. doi: 10.1080/02331930601120086
   Web of Science ®Google Scholar
• Luu DV. Higher-order efficiency conditions via higher-order tangent cones. Numer Funct Anal Optim. 2014;35:68–84. doi: 10.1080/01630563.2013.809583
   Web of Science ®Google Scholar
• Luu DV. Necessary and sufficient conditions for efficiency via convexificators. J Optim Theory Appl. 2014;160:510–526. doi: 10.1007/s10957-013-0377-6
   Web of Science ®Google Scholar
• Luu DV, Mai TT. Optimality and duality in constrained interval-valued optimization. 4OR- Q J Oper Res. 2018;16:311–337. doi: 10.1007/s10288-017-0369-8
   Web of Science ®Google Scholar
• Luu DV, Su TV. Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints. RAIRO – Oper Res. 2018;52:543–559. doi: 10.1051/ro/2017042
   Web of Science ®Google Scholar
• Penot JP. Second order conditions for optimization problems with constraints. SIAM J Control Optim. 1999;37:303–318. doi: 10.1137/S0363012996311095
   Web of Science ®Google Scholar
• Su TV. Optimality conditions for vector equilibrium problems in terms of contingent epiderivatives. Numer Funct Anal Optim. 2016;37:640–665. doi: 10.1080/01630563.2016.1155158
   Web of Science ®Google Scholar
• Su TV. New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces. 4OR- Q J Oper Res. 2018;16(2):173–198. doi: 10.1007/s10288-017-0360-4
   Web of Science ®Google Scholar
• Su TV. Second-order efficiency conditions for C1,1-vector equilibrium problems in terms of contingent derivatives and applications. J Nonlinear Var Anal. 2019;3(3):317–332.
   Web of Science ®Google Scholar
• Su TV. New second-order optimality conditions for vector equilibrium problems with constraints in terms of contingent derivatives. Bull Braz Math Soc New Series. 2019. DOI:10.1007/s00574-019-00157-w
   Web of Science ®Google Scholar
• Su TV, Hang DD. Optimality conditions for the efficient solutions of vector equilibrium problems with constraints in terms of directional derivatives and applications. Bull Iran Math Soc. 2019;45(6):1619–1650. doi: 10.1007/s41980-019-00219-1
   Web of Science ®Google Scholar
• Su TV, Hien ND. Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives. Optim Eng. 2019. DOI:10.1007/s11081-019-09464-z
   Google Scholar
• Wu ZL, Wu SY. Characterizations of the solution sets of convex programs and variational inequality problems. J Optim Theory Appl. 2006;130:341–360. doi: 10.1007/s10957-006-9108-6
   Web of Science ®Google Scholar
• Luu DV. Optimality conditions for local efficient solutions of vector equilibrium problems via convexificators and applications. J Optim Theory Appl. 2016;171:643–665. doi: 10.1007/s10957-015-0815-8
   Web of Science ®Google Scholar
• Giorgi G, Guerraggio A. On the notion of tangent cone in mathematical programming. Optimization. 1992;25:11–23. doi: 10.1080/02331939208843804
   Google Scholar
• Rockafellar RT. Convex analysis. Princeton: Princeton University Press; 1970.
   Google Scholar
• Ioffe AD. Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps. Nonlinear Anal. 1984;8:517–539. doi: 10.1016/0362-546X(84)90091-9
   Web of Science ®Google Scholar
• Demyanov VF, Rubinov AM. Constructive nonsmooth analysis. Frankfurt am Main: Peter Lang; 1995.
   Google Scholar
• Giorgi G, Guerraggio A, Thierfelder J. Mathematics of optimization: smooth and nonsmooth case. Amsterdam: Elsevier; 2004.
   Google Scholar
• Ursescu C. Tangent sets calculus and necessary conditions for extremality. SIAM J Control Optim. 1982;20:563–574. doi: 10.1137/0320041
   Web of Science ®Google Scholar