We establish Fritz John necessary conditions for local weak efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives. Under suitable constraint qualifications, Karush–Kuhn–Tucker necessary conditions for those solutions are investigated.
Mots clés : Vector equilibrium problems, Local weak efficient solutions, Constraint qualifications, Fritz John and Karush–Kuhn–Tucker efficiency conditions
@article{RO_2018__52_2_543_0, author = {Luu, Do Van and Su, Tran Van}, title = {Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {543--559}, publisher = {EDP-Sciences}, volume = {52}, number = {2}, year = {2018}, doi = {10.1051/ro/2017042}, mrnumber = {3880543}, zbl = {1398.90201}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2017042/} }
TY - JOUR AU - Luu, Do Van AU - Su, Tran Van TI - Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 543 EP - 559 VL - 52 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017042/ DO - 10.1051/ro/2017042 LA - en ID - RO_2018__52_2_543_0 ER -
%0 Journal Article %A Luu, Do Van %A Su, Tran Van %T Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 543-559 %V 52 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017042/ %R 10.1051/ro/2017042 %G en %F RO_2018__52_2_543_0
Luu, Do Van; Su, Tran Van. Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 543-559. doi : 10.1051/ro/2017042. http://www.numdam.org/articles/10.1051/ro/2017042/
[1] Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions, in: Advances in Mathematics Supplementary Studies. Academic Press, New York (1981) 160–232 | MR | Zbl
,[2] Set-Valued Analysis. Birkhauser, Boston (1990) | MR | Zbl
and ,[3] Lagrange multipliers and infinite-dimensional equilibrium problems. J. Glob. Optim. 40 (2008) 65–70 | DOI | MR | Zbl
,[4] Lectures on Mathematical Theory of Extremum Problems. Springer–Verlag, Berlin, Heidenberg (1972) | DOI | MR | Zbl
,[5] On the theory of vector optimization and variational inequalities, image space analysis and separation, in: Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, edited by . Kluwer, Dordrecht (2000) 153–215 | DOI | MR | Zbl
, and ,[6] Optimality conditions for vector equilibrium problems. J. Math. Anal. Appl. 342 (2008) 1455–1466 | DOI | MR | Zbl
,[7] Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal. 73 (2010) 3598–3612 | DOI | MR | Zbl
,[8] First order optimality conditions in vector optimization involving stable functions. Optimization 57 (2008) 449–471 | DOI | MR | Zbl
and ,[9] Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives. J. Math. Anal. Appl. 352 (2009) 788–798 | DOI | MR | Zbl
, and ,[10] Contingent epiderivatives and set-valued optimization. Math. Meth. Oper. Res. 46 (1997) 193–211 | DOI | MR | Zbl
and ,[11] Contingent derivatives of set-valued maps and applications to vector optimization. Math. Program. 50 (1991) 99–111 | DOI | MR | Zbl
,[12] Convexificators and necessary conditions for efficiency. Optimization 63 (2014) 321–335 | DOI | MR | Zbl
,[13] Necessary and sufficient conditions for efficiency via convexificators. J. Optim. Theory Appl. 160 (2014) 510–526 | DOI | MR | Zbl
,[14] On optimality conditions for vector variational inequalities. J. Math. Anal. Appl. 412 (2014) 792–804 | DOI | MR | Zbl
and ,[15] Efficient solutions and optimality conditions for vector equilibrium problems. Math. Methods Oper. Res. 79 (2014) 163–177 | DOI | MR | Zbl
and ,[16] Optimality conditions for vector equilibrium problems in normed spaces. Optimization 60 (2011) 1441–1455 | DOI | MR | Zbl
and ,[17] A generalized derivative for calm and stable functions. Diff. Integ. Equ. 5 (1992) 433–454 | MR | Zbl
and ,[18] Scalarization and Kuhn-Tucker-like conditions for weak vector generalized quasivariational inequalities. J. Optimiz. Theory Appl. 130 (2006) 309–316 | DOI | MR | Zbl
and ,[19] Equilibrium conditions and vector variational inequalities: a complex relation. J. Glob. Optimiz. 40 (2008) 353–360 | DOI | MR | Zbl
,[20] Convex Analysis. Princeton University Press, Princeton (1970) | DOI | MR | Zbl
,[21] About contingent epiderivatives. J. Math. Anal. Appl. 327 (2007) 745–762 | DOI | MR | Zbl
and ,[22] Variational characterizations of the contingent epiderivatives. J. Math. Anal. Appl. 335 (2007) 1374–1382 | DOI | MR | Zbl
and ,[23] Optimality conditions for vector equilibrium problems in terms of contingent epiderivatives. Numer. Funct. Anal. Optimiz. 37 (2016) 640–665 | DOI | MR | Zbl
,Cité par Sources :