Necessary optimality conditions for a set valued fractional programming problem in terms of contingent epiderivatives

• Autorzy: Gadhi A. N. , Idrissi M. El.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we are concerned with a multi-objective fractional extremal programming problem. Using the concept of subdifferential of cone-convex set valued mappings, introduced by Baier and Jahn (1999), together with the convex separation principle, we give necessary optimality conditions. An example illustrating the usefulness of our results is also provided.

Słowa kluczowe

EN

fractional optimization; multi-objective optimization; cone-convex mapping; optimality conditions; subdifferential

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2018
• Tom: Vol. 47, no. 2
• Strony: 147--156

Twórcy

autor

Gadhi A. N.

• LSO, Department of Mathematics, Dhar El Mehrez, Sidi Mohamed Ben Abdellah University, B.P. 5605 Sidi Brahim Fes, Morocco

autor

Idrissi M. El.

• LSO, Department of Mathematics, Dhar El Mehrez, Sidi Mohamed Ben Abdellah University, B.P. 5605 Sidi Brahim Fes, Morocco

Bibliografia

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• [3] Bao, T. Q., Gupta, P. and Mordukhovich, B. S. (2007) Necessary conditions in multiobjective optimization with equilibrium constraints. Journal of Optimization Theory and Applications, 135, 179–203.
• [4] Corley, H. W. (1988) Optimality conditions for maximization of set-valued functions. Journal of Optimization Theory and Applications, 58, 1–10.
• [5] Gadhi, N. and Metrane, A. (2004) Sufficient Optimality Condition for Vector Optimization Problems under D.C. Data. Journal of Global Optimization, 28, 55–66.
• [6] Gadhi, N. (2005) Optimality conditions for the difference of convex set-valued mappings. Positivity, 9, 687–703.
• [7] Gadhi, N. (2008) Necessary and sufficient optimality conditions for fractional multi-objective problems. Optimization, 57, 527–537.
• [8] Hiriart-Urruty, J. B. (1989) From Convex Optimization to Nonconvex Optimization. In: F.H. Clarke, V.F. Demyanov, F. Giannessi, eds., Nonsmooth Optimization and Related Topics, Plenum Press, 219–239.
• [9] Jahn, J. and Rauh, R. (1997) Contingent epiderivatives and set-valued optimization. Mathematical Methods of Operations Research, 46, 193–211.
• [10] Liang, Z. A., Huang, H. X. and Pardalos, P. M. (2001) Optimality conditions and duality for a class of nonlinear fractional programming problems. Journal of Optimization Theory and Applications, 110, 611– 619.
• [11] Mordukhovich, B.S. (2006) Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications. Grundlehren Series (Fundamental Principles of Mathematical Sciences), 330 and 331, Springer, Berlin.
• [12] Sawaragi, Y. and Tanino, T. (1980) Conjugate maps and duality in multiobjective optimization. Journal of Optimization Theory and Applications, 31, 473–499.
• [13] Taa, A. (2003) Subdifferentials of multifunctions and Lagrange multipliers for multiobjective optimization. Journal of Mathematical Analysis and Applications, 283, 398–415.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).