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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)
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