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两层多人多目标决策模型及其凸性 总被引:1,自引:0,他引:1
王先甲 《高校应用数学学报(A辑)》1995,(3):349-357
本文提出了四种一般性两层多人多目标决策模型及其最优解概念,它们适应于下层以不同已知信息提供给上层并涉及多个决策者不同偏好的两层多目标决策问题,研究了与这些模型相关的几种集值函数(包括下层有效前沿面,下层目标空间构成的集值函数和上层的两种复合目标集值函数)在各种意义下的凸性。 相似文献
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本文主要讨论Asplund空间的一些几何特征。设 X 为 Banach 空间,本文证明了下述等价:(1)X 是 Asplund 空间;(2)X~*的每个有界范闭子集包含它的ω~*闭凸包的一个端点;(3)X~*的每个有界范闭子集包含它的凸包的一个端点;(4)对 X~*的每个有界范闭子集 A,存在 x_o∈X/{0}和 x_o~*∈A,使得 x_o~*(x_o)=(?)x~*(x_o);(5)对 X~*的每个有界范闭子集 A,集{x∈X,■x_o~*∈A,使得 x_o~*(x)=sup x~*(x)}在 X 中范稠 相似文献
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本文在自反Banach空间中引进了锥弱连续映射和点集的弱连通概念.在讨论锥弱连续和锥拟凸映射以及锥最小上界的几个性质的基础上,证明了当象集为锥凸集时定义在自反Ba- nach空间中的有界闭凸集上的锥弱连续和锥拟凸映射多目标最优化问题的锥有效解集是弱连通的. 相似文献
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应用丁协平在FC-空间内对集值映象证明的极大元存在性定理,在没有凸性结构的FC-空间内对广义拟变分包含(不包含)问题组的解证明了某些新的存在性定理.这些结果在较弱的条件下改进和推广了最近文献中的某些结果从拓朴矢量空间的闭凸子集到FC-空间. 相似文献
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本文提出了多目标决策偏好及最优解的一般概念和集诱导偏好的概念.给出了判断ρ-完备集的一系列条件,从而指出了ρ-完备集是十分广泛的集类.得到了集合的Λ-有效点的存在性定理和ρ-下闭集与截面的Λ-有效点的性质.通过引入函数Λ-下半连续的概念,得到了多目标决策一般集诱导偏好最优解的存在性定理.在这些结果的基础上,最后得到了集合Y关于Λ和多目标决策问题的控制性质. 相似文献
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Banach空间中关于有界集的同时远达问题的适定性 总被引:7,自引:1,他引:6
本文研究Banach空间中关于有界集的同时远达问题的适定性,在集合的Hausdorff距离下,证明了:对自反局部一致凸Banach空间中的闭有界集K,使所有关于K的同时远达问题是适定的紧凸子集A全体在紧凸子集全体中是Gδ型集. 相似文献
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设C是实Banach空间X中有界闭凸子集且O是C的内点,G是X中非空有界闭的相对弱紧子集.记K(X)为X的非空紧凸子集并赋Hausdorff距离.称广义共同远达点问题maxc(A,G)是适定的是指它有唯一解(x0,z0)且它的每个极大化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下,我们运用不同于DeBlasi,MyjalandPapini和Li等人的方法证明了集{A∈K(X);maxc(A,G)是适定的}含有K(X)中稠Gδ集,这本质地推广和延拓了包括DeBlasi,MyjakandPapini和Li等人在内的近期相应结果. 相似文献
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姚志敏 《纯粹数学与应用数学》2017,33(1)
使用切面技术、归纳法等证明了欧氏空间中凸集极点的存在性,进一步证明了空间中一般有界闭凸集(不只局限于凸多面体)中任意一点同样可表示为极点的凸组合.方法独到. 相似文献
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An interactive approach for solving bi-objective optimisation problems with multiple decision-makers in a context where the decisions are made via the strict majority voting rule is proposed. An adequate use of projection and decomposition techniques leads to a hierarchical algorithm in which the upper level is represented by a relaxed version of the bi-objective problem in the objective space. The feasibility of the partial consensus obtained in the upper (decision) level by the strict majority voting rule is tested in the lower (analysis) level of the algorithm. Some properties of the relaxed bi-objective problem allow that different preference structures of the decision-makers can be represented by appropriate multiobjective methods. The paper includes numerical examples that illustrate the characteristics of the approach proposed. 相似文献
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In this paper the Pareto efficiency of a uniformly convergent multiobjective optimization sequence is studied. We obtain some relation between the Pareto efficient solutions of a given multiobjective optimization problem and those of its uniformly convergent optimization sequence and also some relation between the weak Pareto efficient solutions of the same optimization problem and those of its uniformly convergent optimization sequence. Besides, under a compact convex assumption for constraints set and a certain convex assumption for both objective and constraint functions, we also get some sufficient and necessary conditions that the limit of solutions of a uniformly convergent multiobjective optimization sequence is the solution of a given multiobjective optimization problem. 相似文献
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In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective
problem is derived. This characterization takes into account the relative position of the gradients of the objective functions
and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any
number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization
of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective
problems is derived, which consists of solving a single linear optimization problem. 相似文献
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In this paper we provide a duality theory for multiobjective optimization problems with convex objective functions and finitely many D.C. constraints. In order to do this, we study first the duality for a scalar convex optimization problem with inequality constraints defined by extended real-valued convex functions. For a family of multiobjective problems associated to the initial one we determine then, by means of the scalar duality results, their multiobjective dual problems. Finally, we consider as a special case the duality for the convex multiobjective optimization problem with convex constraints. 相似文献
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Gert Wanka 《Journal of Mathematical Analysis and Applications》2002,275(1):354-368
In this paper we present a duality approach for a multiobjective fractional programming problem. The components of the vector objective function are particular ratios involving the square of a convex function and a positive concave function. Applying the Fenchel-Rockafellar duality theory for a scalar optimization problem associated to the multiobjective primal, a dual problem is derived. This scalar dual problem is formulated in terms of conjugate functions and its structure gives an idea about how to construct a multiobjective dual problem in a natural way. Weak and strong duality assertions are presented. 相似文献
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拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性 总被引:3,自引:0,他引:3
本文研究局部凸的Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性问题。利用广义鞍点定理,证明了目标映射为一对一的锥拟凸多目标规划的锥有效解集是连通的。 相似文献
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We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build
a family of convex scalar strict representations of a convex map F from R
n
to R
m
with respect to the lexicographic order on R
m
and we add a variant of the logarithmic-quadratic regularization of Auslender, where the unconstrained variables in the domain
of F are introduced in the quadratic term. The nonegative variables employed in the scalarization are placed in the logarithmic
term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak pareto solution of
the multiobjective optimization problem. 相似文献
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不完全信息群体多属性决策的过滤函数法 总被引:3,自引:0,他引:3
对于不完全信息群体多属性决策问题,本文通过构造适当的过滤函数,充分利用高质量的信息和过滤掉低质量的信息,使效用信息的集结过程充分体现群体的意愿.在引进一致优、严格优和弱优等偏好指标的基础上,利用它们建立起方案集上合理的全序关系,从而构造了一个交互式的群体多属性决策方法. 相似文献
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In a general normed space, we consider a piecewise linear multiobjective optimization problem. We prove that a cone-convex piecewise linear multiobjective optimization problem always has a global weak sharp minimum property. By a counter example, we show that the weak sharp minimum property does not necessarily hold if the cone-convexity assumption is dropped. Moreover, under the assumption that the ordering cone is polyhedral, we prove that a (not necessarily cone-convex) piecewise linear multiobjective optimization problem always has a bounded weak sharp minimum property. 相似文献
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魏紫銮 《应用数学学报(英文版)》2001,17(3):366-374
1. IntroductionThe quadratic programming (QP) problem is the most simple one in nonlinear pro-gramming and plays a very important role in optimization theory and applications.It is well known that matriX splitting teChniques are widely used for solving large-scalelinear system of equations very successfully. These algorithms generate an infinite sequence,in contrast to the direct algorithms which terminate in a finite number of steps. However,iterative algorithms are considerable simpler tha… 相似文献