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Abstrakty
In this paper, we are concerned with a constrained set-valued optimization problem (P). Using support functions, we give necessary optimality conditions in terms of Karush-Kuhn-Tucker (KKT) multipliers and approximations. Under generalized convex- ity, we investigate sufficient optimality conditions. An example illustrating our findings is also given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
439--452
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- LAMA, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Department of Mathematics, Fes, Morocco
autor
- LAMA, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Department of Mathematics, Fes, Morocco
autor
- LAMA, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Department of Mathematics, Fes, Morocco
Bibliografia
- Allali, K. and Amahroq, T. (1997) Second order approximations and primal and dual necessary optimality conditions. Optimization 40, 229–246.
- Amahroq, T. and Taa, A. (1997) On Karush-Kuhn-Tucker multipliers for multiobjective optimization problems. Optimization 41 , 159–172.
- Amahroq, T. and Gadhi, N. (2001) On the regularity conditions for vector programming problems. J. Glob. Optim. 21, 435–443.
- Amahroq, T. and Gadhi, N. (2003) Second order optimality conditions for the extremal problem under inclusion constraints. J. Math. Anal. Appl. 285, 74–85
- Amahroq, T. and Taa, A. (1997) Sufficient conditions of optimality for multiobjective optimization problems with -paraconvex data. Studia Mathematica 124, 239–247.
- Bazine, M., Bennani, A., Gadhi, N. and Lafhim, L. (2011) Optimality and Duality for Non-Lipschitz Multiobjective Optimization Problems. Numerical Functional Analysis and Optimization 32, 142–154.
- Ciligot-Travain, M. (1994) On Lagrange Kuhn Tucker multipliers for Pareto optimization problem. Numerical Functional Analysis and Optimization 15, 689–693.
- Chuong, T.D. and Kim, D.S. (2014) Optimality conditions and duality in nonsmooth multiobjective optimization problems. Ann. Oper. Res. 217, 117–136.
- Corley, H.W. (1988) Optimality conditions for maximization of set-valued functions. J. Optim. Theory Appl. 58, 1–10.
- Dempe, S. and Gadhi, N. (2010) Second order optimality conditions for bilevel set optimization problems. J. Glob. Optim. 47, 233–245.
- Dutta, J. and Chandra, S. (2004) Convexificator, generalized convexity and vector optimization. Optimization 53, 77–94.
- Gadhi, N. (2005a) Necessary optimality conditions for Lipschitz multiobjective optimization problems. Georgian Mathematical Journal 12, 65–74.
- Gadhi, N. (2005b) Optimality conditions for the difference of convex set-valued mappings. Positivity 9, 687–703.
- Gadhi, N., Jawhar, A. (2013) Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints. J. Glob. Optim. 56, 489–501.
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- Khanh, P. Q. and Dinh, N. T. (2008) First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization. Appl Math Optim. 58, 147–166.
- Khanh, P. Q. and Tung, L.T. (2003) First and second-order optimality conditions using approximations for vector equilibrium problems with constraints. J. Glob. Optim. 55, 901–920.
- Khanh, P. Q. and Tuan, N. D. (2006) First and second order optimality conditions using approximations for nonsmooth vector optimization in Banach spaces. J. Optim. Theory Appl. 130, 289–308.
- Kwan, D. B. and Kim, D. S. (2011) Optimality and duality theorems in nonsmooth multiobjective optimization. Fixed Point Theory and Appl 42, 1–11.
- Luc, D.T. (1991) Contingent derivatives of set-valued maps and applications to vector optimization. Math. Program. 50, 99–111.
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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