共查询到16条相似文献,搜索用时 91 毫秒
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二层广义凸规划及其性质 总被引:4,自引:0,他引:4
讨论了二层规划的性质 ,在一些凸性和广义凸性假设下 ,讨论了下层极值函数和上层目标函数的凸性、拟凸性和连续性性质 ,获得了五个定理 ,并予以证明 . 相似文献
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本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 . 相似文献
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无限维空间拟凸映射多目标最优化问题解集的连通性 总被引:11,自引:1,他引:10
本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射。并在约束集为紧凸条件下,证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果。 相似文献
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二层凸规划的基本性质 总被引:2,自引:0,他引:2
本文研究了一类抛述二层决策问题的二层数学规划模型,在一定条件下讨论了下层极值函数和上层复合目标函数的凸性和连续性,给出了二层决策问题优决策的存在条件。 相似文献
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若记B^n为C^n中的单位球,本文研究B^n上的强拟凸映强,(1)强拟凸映照与星形映照及凸映照的关系,(2)强拟凸映照的二次项系;(3)单位多圆柱上的强拟凸映照。 相似文献
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研究具有一般形式的凸二次-线性双层规划问题。讨论了这类双层规划问题的DC规划等价形式,利用DC规划共轭对偶理论,提出了凸二次-线性双层规划的共轭对偶规划,并给出相应的对偶性质。 相似文献
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Masatoshi Sakawa Hideki Katagiri 《Central European Journal of Operations Research》2012,20(1):101-117
This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal
with the formulated fuzzy random two-level linear programming problem, an α-stochastic two-level linear programming problem is defined through the introduction of α-level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced
and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each
fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming
problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced
and a numerical example is provided to illustrate the proposed method. 相似文献
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A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming 总被引:2,自引:0,他引:2
In this paper, on the basis of the logarithmic barrier function and KKT conditions , we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method. 相似文献
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On an algorithm solving two-level programming problems with nonunique lower level solutions 总被引:2,自引:0,他引:2
In the paper, an algorithm is presented for solving two-level programming problems. This algorithm combines a direction finding problem with a regularization of the lower level problem. The upper level objective function is included in the regularzation to yield uniqueness of the follower's solution set. This is possible if the problem functions are convex and the upper level objective function has a positive definite Hessian. The computation of a direction of descent and of the step size is discussed in more detail. Afterwards the convergence proof is given.Last but not least some remarks and examples describing the difficulty of the inclusion of upper-level constraints also depending on the variables of the lower level are added. 相似文献
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《Optimization》2012,61(5):1285-1303
The theory of Ky Fan minimax inequalities provides a powerful general framework for the study of convex programming, variational inequalities and economic equilibrium problems. One of the fundamental methods for finding a solution of Ky Fan minimax inequalities is the proximal point algorithm, where a lot of papers have been dedicated to this subject. In this paper, a general class of two-level hierarchical Ky Fan minimax inequalities is introduced in real Hilbert spaces. For a wide class of Bregman functions, an association of inexact implicit Bregman-penalization proximal and Bregman-splitting proximal algorithms are suggested and analysed. Weak and strong convergences are proved under essentially weaker conditions. We conclude this paper with a hierarchical minimization problem and a numerical example. 相似文献
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In the research of mathematical programming, duality theorems are essential and important elements. Recently, Lagrange duality theorems for separable convex programming have been studied. Tseng proves that there is no duality gap in Lagrange duality for separable convex programming without any qualifications. In other words, although the infimum value of the primal problem equals to the supremum value of the Lagrange dual problem, Lagrange multiplier does not always exist. Jeyakumar and Li prove that Lagrange multiplier always exists without any qualifications for separable sublinear programming. Furthermore, Jeyakumar and Li introduce a necessary and sufficient constraint qualification for Lagrange duality theorem for separable convex programming. However, separable convex constraints do not always satisfy the constraint qualification, that is, Lagrange duality does not always hold for separable convex programming. In this paper, we study duality theorems for separable convex programming without any qualifications. We show that a separable convex inequality system always satisfies the closed cone constraint qualification for quasiconvex programming and investigate a Lagrange-type duality theorem for separable convex programming. In addition, we introduce a duality theorem and a necessary and sufficient optimality condition for a separable convex programming problem, whose constraints do not satisfy the Slater condition. 相似文献
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Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility 总被引:1,自引:0,他引:1
This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods. 相似文献