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1.
多目标锥—广义凸规划有效解的充要条件   总被引:2,自引:0,他引:2  
王秋庭  王先甲 《数学杂志》1993,13(4):483-490
本文提出了n维欧氏空间上的锥-凸、锥-伪凸、锥-拟凸向量值函数的概念,讨论了它们之间的关系,并在此基础上,对多目标数学规划问题关于凸锥∧有效解,撇开约束品性,讨论了它的充分必要条件。  相似文献   

2.
多目标规划锥有效解的最优性条件   总被引:1,自引:0,他引:1  
该文提出了广义锥凸向量函数以及向量函数关于锥八的下降、不变、非升、非降方向集等概念.在讨论它们的性质和判别条件的基础上,给出了决策可行集中的点为锥八一有效解的一系列充分必要条件.  相似文献   

3.
本文研究带不等式和等式约束的多目标规划的Mond-Weir型对偶性理论。在目标和约束是广义凸的假设下,证明了弱对偶定理、直接对偶定理以及逆对偶定理。  相似文献   

4.
多目标规划的圆锥有效解   总被引:2,自引:0,他引:2  
本文利用有限维向量空间中圆锥的概念,引入了多目标规划问题的一种新的有效解-圆锥有效解,并讨论了这种有效解的性质。同时,讲座了圆锥有效解与Pareto有效解以及绝对最优解之间的关系。最后,通过引进目标总值差异概念,分析了圆锥有效解的主要特点。  相似文献   

5.
多目标规划ak—较多有效解类的若干性质   总被引:8,自引:0,他引:8  
在(1)中,作者提出多目标规划的较多有效解和较多最优解概念,并研究了它们的基本性质,文(3)则讨论k-较多最优解的若干性质。文(4)利用较多序类进一步引进多目标规划问题的ak-较多有效解,并证明了这类解的最优性必要条件。本文再给出多目标规划问题的ak-较多最优解的概念,并讨论了多目标规划ak-较多有效解和ak-较多最优解的若干重要性质。  相似文献   

6.
对于赋范线性空间中的多目标规划问题,引进了广义KT-真有效解的概念.在一定条件下,得到了广义KT-真有效解和广义H-局部真有效解之间的关系.  相似文献   

7.
多目标规划αk-较多有效解类的有效性充分条件   总被引:7,自引:0,他引:7  
在文[3]引进多目标规划总是的带双参数α和k的αk-较多有效解,并且给出了此类解的有效性必要条件。本文在一定凸性的假设下证明了αk-较多有效解和αk-弱较多有效解的几个有效性充分条件。  相似文献   

8.
求解群体多目标凸规划的一个交互规划算法   总被引:3,自引:0,他引:3  
本文给出一个由决策群体求解带有非线性约束的多目标凸规划问题的交互规划算法。此法通过决策群体与分析者之间以及各决策者之间的交互,最终得到群体满意的有效解,本文还证明了这一算法的收敛性定理。  相似文献   

9.
本文提出一个新的约束规格,导出可微多目标规划的有效解的Kuhn-Tucker必要条件,并证明在此条件下,有效解是Kuhn-Tucker真有效解。  相似文献   

10.
本文利用Ben-Tal广义代数运算对一类可微及不可微半无限多目标规划进行了讨论。在目标及约束为(h,)─—凸的情况下得出了有效解的几个充分条件。  相似文献   

11.
In this work, we present a new set-oriented numerical method for the numerical solution of multiobjective optimization problems. These methods are global in nature and allow to approximate the entire set of (global) Pareto points. After proving convergence of an associated abstract subdivision procedure, we use this result as a basis for the development of three different algorithms. We consider also appropriate combinations of them in order to improve the total performance. Finally, we illustrate the efficiency of these techniques via academic examples plus a real technical application, namely, the optimization of an active suspension system for cars.The authors thank Joachim Lückel for his suggestion to get into the interesting field of multiobjective optimization. Katrin Baptist as well as Frank Scharfeld helped the authors with fruitful discussions. This work was partly supported by the Deutsche Forschungsgemeinschaft within SFB 376 and SFB 614.  相似文献   

12.
In this note, we present a geometrical characterization of the set of weakly efficient points in constrained convex multiobjective optimization problems, valid for a compact set of objectives.  相似文献   

13.
An example of design might be a warehouse floor (represented by a setS) of areaA, with unspecified shape. Givenm warehouse users, we suppose that useri has a known disutility functionf isuch thatH i(S), the integral off iover the setS (for example, total travel distance), defines the disutility of the designS to useri. For the vectorH(S) with entriesH i(S), we study the vector minimization problem over the set {H(S) :S a design} and call a design efficient if and only if it solves this problem. Assuming a mild regularity condition, we give necessary and sufficient conditions for a design to be efficient, as well as verifiable conditions for the regularity condition to hold. For the case wheref iis thel p-distance from warehouse docki, with 1<p<, a design is efficient if and only if it is essentially the same as a contour set of some Steiner-Weber functionf =1 f 1++ m f m ,when the i are nonnegative constants, not all zero.This research was supported in part by the Interuniversity College for PhD Studies in Management Sciences (CIM), Brussels, Belgium; by the Army Research Office, Triangle Park, North Carolina; by a National Academy of Sciences-National Research Council Postdoctorate Associateship; and by the Operations Research Division, National Bureau of Standards, Washington, D.C. The authors would like to thank R. E. Wendell for calling Ref. 16 to their attention.  相似文献   

14.
1 引言广义极大极小问题在工程优化设计、电子线路优化设计、计算机辅助设计及最优控制中有着广泛的应用.由于广义极大极小问题是一类拟可微问题,所以我们可以采用针对拟可微函数的算法来求解,见文[4].另外,在一定条件下,广义有限极大极小问题还可以转化为光滑约束的非线性规划问题[3].但到目前为止,大多数算法仅考虑广义有限极大  相似文献   

15.
Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn–Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated.  相似文献   

16.
对一般目标函数极小化问题的拟牛顿法及其全局收敛性的研究,已经成为拟牛顿法理论中最基本的开问题之一.本文对这个问题做了进一步的研究,对无约束优化问题提出一类新的广义拟牛顿算法,并结合Goldstein线搜索证明了算法对一般非凸目标函数极小化问题的全局收敛性.  相似文献   

17.
对广义几何规划问题(GGP)提出了一个确定型全局优化算法,这类优化问题能广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中,使用指数变换及对目标函数和约束函数的线性下界估计,建立了GGP的松弛线性规划(RLP),通过对RLP可行域的细分以及一系列RLP的求解过程,从理论上证明了算法能收敛到GGP的全局最优解,对一个化学工程设计问题应用本文算法,数值实验表明本文方法是可行的。  相似文献   

18.
We give an example to illustrate a gap between multiobjective optimization and single-objective optimization, which solves a problem proposed in Ref. 1.  相似文献   

19.
Two types of rod antennas of mobile phones are optimized so that the radiated energy absorbed by the head or body of the user is reduced and the radiation intensity to other areas especially to the receiver is increased. The mathematical modelling of this problem leads to an infinite dimensional bicriterial optimization problem. It is shown that this optimization problem and a discretized version of this problem are solvable. The relationship between the infinite and finite dimensional optimization problem is investigated. Numerical results are presented for mobile phones working with the GSM standards 900 and 1800.  相似文献   

20.
We establish both necessary and sufficient optimality conditions for weak efficiency and firm efficiency by using Hadamard directional derivatives and scalarizing the multiobjective problem under consideration via signed distances. For the first-order conditions, the data of the problem need not even be continuous; for the second-order conditions, we assume only that the first-order derivatives of the data are calm. We include examples showing the advantages of our results over some recent papers in the literature. This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The authors are indebted to Professor P.L. Yu and two anonymous referees for many valuable remarks, which helped improving the previous version of the paper.  相似文献   

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