| 多目标规划的像问题及其应用 |
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| 引用本文： | 黄平,于寅.多目标规划的像问题及其应用[J].华中科技大学学报(自然科学版),1992(Z1). |
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| 作者姓名： | 黄平 于寅 |
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| 作者单位： | 赣南师范学院
(黄平)，华中理工大学数学系(于寅) |
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| 摘 要： | 设X,Y,Z皆为拓扑向量空间,C和D分别是Y和Z中的闭凸锥.Z中由D规定的偏序如下:对任意z_1,z_2∈Z,当且仅当z_2-z_1∈D时,z_1≤z_2考虑下述多目标规划问题min f(x);s.t.x∈R(?){x ∈X且g(x)∈C},其中,f:X→Z;g:X→Y.定义1 设(?)∈R,如果(f(?)-D)∩(f(R)\{f(?)}=?,则f(?)称为(1)式的有效点.当f(?)是(1)式的有效点时,称(?)是(1)式的有效解.任给(?)∈R,作映射F(?):X→Z×Y为F(?)(x)=(f(?)-f(x)),g(x)).记H=(D\{0})×C,K(?)={F(?)(x)|x∈X},E(?)=K(?)-c1H.定义2称
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On the Image of Multi-objective programming and Its Application |
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| Huang Ping Yu Yin.On the Image of Multi-objective programming and Its Application[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,1992(Z1). |
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| Authors: | Huang Ping Yu Yin |
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| Institution: | Huang Ping Yu Yin |
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| Abstract: | The concept of image of single objective programming is generalized to the problem of multiple objective programming. The image of multiple objective programming is defined and a theorem concerning the relation between the effective point sets of multiple objective programming and its image problem is proved. As an application of the theorem, an existence theorem of the effective solution using D completeness is also given. |
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| Keywords: | multi-objective programming image problem D completeness |
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