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Second order duality in multiobjective programming involving generalized type I functions. (English) Zbl 1071.90042
Summary: Recently Hachimi and Aghezzaf introduced the notion of (\(F, \alpha, \rho, d\))-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, we extend the notion of (\(F, \alpha, \rho, d\))-type I functions to second order and establish several mixed duality results under second order generalized (\(F, \alpha, \rho, p, d\))-type I functions. Our results generalize the duality results recently given by B. Aghezzaf [J. Math. Anal. Appl. 285, 97–106 (2003; Zbl 1089.90047)] and M. Hachimi and B. Aghezzaf [J. Math. Anal. Appl. 296, 382–392 (2004; Zbl 1113.90142)].

MSC:
90C29 Multi-objective and goal programming
90C25 Convex programming
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References:
[1] Abadie, J. 1967.On Kuhn-Tucker Theorem, in Nonlinear ProgrammingEdited by: Abadie, J. 21–36. North Holland: Amsterdam.
[2] DOI: 10.1016/S0022-247X(03)00359-7 · Zbl 1089.90047 · doi:10.1016/S0022-247X(03)00359-7
[3] DOI: 10.1023/A:1008321026317 · Zbl 0970.90087 · doi:10.1023/A:1008321026317
[4] DOI: 10.1016/j.jmaa.2003.12.042 · Zbl 1113.90142 · doi:10.1016/j.jmaa.2003.12.042
[5] DOI: 10.1007/BF02207775 · Zbl 0797.90082 · doi:10.1007/BF02207775
[6] DOI: 10.1007/BF02207776 · Zbl 0797.90083 · doi:10.1007/BF02207776
[7] DOI: 10.1016/0022-247X(75)90111-0 · Zbl 0313.90052 · doi:10.1016/0022-247X(75)90111-0
[8] Mond B., Proceedings of Optimization Miniconference pp 89– (1995)
[9] DOI: 10.1016/0022-247X(92)90303-U · Zbl 0764.90074 · doi:10.1016/0022-247X(92)90303-U
[10] DOI: 10.1016/0022-247X(88)90313-7 · Zbl 0647.90076 · doi:10.1016/0022-247X(88)90313-7
[11] Sawaragi Y., Theory of Multiobjective Optimization (1985) · Zbl 0566.90053
[12] Zhang J., Proceedings of Optimization Miniconference III pp 79– (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.