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2008 | 6 | 3 | 453-468
Tytuł artykułu

Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
3
Strony
453-468
Opis fizyczny
Daty
wydano
2008-09-01
online
2008-07-02
Twórcy
autor
autor
autor
Bibliografia
  • [1] Adán M., Novo V., Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness, European J. Oper. Res, 2003, 149, 641–653 http://dx.doi.org/10.1016/S0377-2217(02)00444-7
  • [2] Arana-Jiménez M., Rufián-Lizana A., Osuna-Gómez R., Weak efficiency for multiobjective variational problems, European J. Oper. Res., 2004, 155, 373–379 http://dx.doi.org/10.1016/S0377-2217(02)00882-2
  • [3] Boţ R.I., Grad S.-M., Wanka G., A new constraint qualification and conjugate duality for composed convex optimization problems, J. Optim. Theory Appl., 2007, 135, 241–255 http://dx.doi.org/10.1007/s10957-007-9247-4
  • [4] Boţ R.I., Hodrea I.B., Wanka G., Farkas-type results for inequality systems with composed convex functions via conjugate duality, J. Math. Anal. Appl., 2006, 322, 316–328 http://dx.doi.org/10.1016/j.jmaa.2005.09.007
  • [5] Boţ R.I., Kassay G., Wanka G., Strong duality for generalized convex optimization problems, J. Optim. Theory Appl., 2005, 127, 45–70 http://dx.doi.org/10.1007/s10957-005-6392-5
  • [6] Boţ R.I., Wanka G., A new duality approach for multiobjective convex optimization problems, J. Nonlinear Convex Anal., 2003, 3, 41–57
  • [7] Boţ R.I., Wanka G., An analysis of some dual problems in multiobjective optimization (I), Optimization, 2004, 53, 281–300 http://dx.doi.org/10.1080/02331930410001715514
  • [8] Boţ R.I., Wanka G., An analysis of some dual problems in multiobjective optimization (II), Optimization, 2004, 53, 301–324 http://dx.doi.org/10.1080/02331930410001715523
  • [9] Boţ R.I., Wanka G., Farkas-type results with conjugate functions, SIAM J. Optim., 2005, 15, 540–554 http://dx.doi.org/10.1137/030602332
  • [10] Combari C., Laghdir M., Thibault L., Sous-différentiels de fonctions convexes composées, Ann. Sci. Math. Québec, 1994, 18, 119–148 (in French)
  • [11] Hiriart-Urruty J.-B., Martínez-Legaz J.-E., New formulas for the Legendre-Fenchel transform, J. Math. Anal. Appl., 2003, 288, 544–555 http://dx.doi.org/10.1016/j.jmaa.2003.09.012
  • [12] Jahn J., Mathematical vector optimization in partially ordered linear spaces, Peter Lang Verlag, Frankfurt am Main, 1986
  • [13] Jeyakumar V., Composite nonsmooth programming with Gâteaux differentiability, SIAM J. Optim., 1991, 1, 30–41 http://dx.doi.org/10.1137/0801004
  • [14] Jeyakumar V., Lee G.M., Dinh N., Characterizations of solution sets of convex vector minimization problems, European J. Oper. Res., 2006, 174, 1396–1413 http://dx.doi.org/10.1016/j.ejor.2005.05.007
  • [15] Jeyakumar V., Yang X.Q., Convex composite minimization with C 1,1 functions, J. Optim. Theory Appl., 1993, 86, 631–648 http://dx.doi.org/10.1007/BF02192162
  • [16] Kutateladže S.S., Changes of variables in the Young transformation, Soviet Math. Dokl., 1977, 18, 1039–1041
  • [17] Lemaire B., Application of a subdifferential of a convex composite functional to optimal control in variational inequalities, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, 1985, 255, 103–117
  • [18] Levin V.L., Sur le Sous-Différentiel de Fonctions Composeé, Doklady Akademia Nauk, 1970, 194, 28–29 (in French)
  • [19] Lin Y., Wang X., Necessary and sufficient conditions of optimality for some classical scheduling problems, European J. Oper. Res., 2007, 176, 809–818 http://dx.doi.org/10.1016/j.ejor.2005.09.017
  • [20] Rockafellar R.T., Convex analysis, Princeton University Press, Princeton, 1970
  • [21] Wanka G., Boţ R.I., Vargyas E., Duality for location problems with unbounded unit balls, European J. Oper. Res., 2007, 179, 1252–1265 http://dx.doi.org/10.1016/j.ejor.2005.09.048
  • [22] Yang X.Q., Jeyakumar V., First and second-order optimality conditions for convex composite multiobjective optimization, J. Optim. Theory Appl., 1997, 95, 209–224 http://dx.doi.org/10.1023/A:1022695714596
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0036-6
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