EQUILIBRIUM ALGORITHMS WITH NONMONOTONE LINE SEARCH TECHNIQUE FOR SOLVING THE TRAFFIC ASSIGNMENT PROBLEMS

This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.     

THE SECOND-ORDER CONDITIONS OF NONDOMINATED SOLUTIONS FOR C~(1,?) GENERALIZED MULTIOBJECTIVE MATHEMATICAL PROGRAMMING

In this paper,the generalized Hessian matrix and the generalized second-order directional(?)erivative for C~(1,1)vector functions are defined.The extension of the vector second-order Taylorexpansion is derived.The second-order necessary and sufficient conditions for the local nondominatedsolutions associated with the given convex cone and polyhedral convex cone of the generalizedmultiobjective mathematical programming problem with C~(1,1)constrained functions are discussed.     

A NEW SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE DFP ALGORITHM WITH WOLFE LINE SEARCH

ＡＮＥＷＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＴＨＥＤＦＰＡＬＧＯＲＩＴＨＭＷＩＴＨＷＯＬＦＥＬＩＮＥＳＥＡＲＣＨ￥ＸＵＤａｃｈｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖ...     

ON THE STRICT EFFICIENCY IN A LOCALLYCONVEX SPACE

1.IntroductionInreference[11,theconceptofstrictefficiency)anewkindofproperefficiency,wasintroductedinvectoroptimizationinarealnormedspace.ThisefficiencyisshowntohavemailydesirablepropertiesandbeanextensionofthesuperefficiencyinthesenseofBorwein[2].Inthispaper,wecontinuethestudyofstrictefficiency.WeeXtendthestrictefficiencyinnormedspacestothecaseinlocallyconvexvectorspaces.Themainpurposeofthepreselltpaperistogiveascalarchaxacterizationofstrictefficiencybyusingakindoffunctional(so--called"base…     

ON VECTOR OPTIMIZATION WHEN THE ORDERING CONE HAS AN EMPTY INTERIOR

1.IntroductionLetXbeavectorspace,Ybeatopologicalvectorspace,Zbealocallyconvexspace,andletthetopologicaldualspacesofYandZbedenotedbyY*andZ*,respectively.LetCbeapointedconvexconeinYandKbeaclosedconvexpointedconeinZ.ThedualconesofCandKaredefinedasrespec...     

THE EXISTENCE OF JENSEN BOUNDARY POINTS IN COMPLEX BANACH SPACES

Inthelasttenyears,severalremarkableresultswereestablishedinthegeometricaltheoryofinfinitelydimensionalcomplexBanachspaces.In[1],A.V.BukhvalovandA.A.DanilevichhaveintroducedtheanalyticRadon--NikodympropertyincomplexBanachspaces,whichcanbeseenastheanalyticanalogueofthewell-knownRadon-NikodympropertyconcerningtherealstructuresofBanachspaces.TheanalyticRadon-Nikodympropertyhasbeenextensivelystudied(see[2--6]),onecancharacterizetheanalyticRadon-Nikodympropertyintermsoftheconvergenceofplurisub…     

层次分析法中区间判断的凸锥模型

用全新凸锥模型讨论层次分析法中常规点判断以及区间判断的权重向量的特性与算法，并对它们给出统一的几何解释．本文提出的交锥与包络锥方法是估算区间判断下权重向量可行域的一种合理而又实用的算法     

判断矩阵凸组合系数的优化原理研究

对判断矩阵凸组系数的优化原理进行了研究 ,给出了判断矩阵最优凸组合系数的求解方法 ,讨论了判断矩阵最优凸组合的性质.     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

模糊合作对策在凸几何上的Shapley函数

首先给出了模糊合作对策在凸几何上的定义。通过相应的公理体系,论述了模糊合作对策在凸几何上的Shapley函数。为了更好了解此类模糊合作对策,研究了两类特殊模糊合作对策在凸几何上的Shapley函数,并证明了其存在性和唯一性,拓展了模糊合作对策的研究范围。最后通过算例分析来具体说明局中人在此类模糊合作对策上的收益值。     

灰色凸关联及其性质

在定义了正离散序列的凹凸性、相对凸度的基础上, 用相关因素之间相对凸度的接近性作为关联程度的度量, 提出了灰色凸关联的概念, 讨论了灰色凸关联的性质. 提出灰色关联序的干扰因素独立性, 证明了本文提出的灰色凸关联序和另外6种灰色关联序具有干扰因素独立性, 邓氏关联度不满足干扰因素独立性. 通过实例说明灰色凸关联度能较好的反映序列间的关联程度.     

判断矩阵的Hadam ard凸组合

给出了具有实际意义的判断矩阵 Hadamard凸组合的定义 ,并证明了判断矩阵 Hadamard凸组合的一个性质 .     

Algorithm Implementation for Distributed Convex Intersection Computation

Intersection computation of convex sets is a typical problem in distributed optimization. In this paper, the algorithm implementation is investigated for distributed convex intersection computation problems. In a multi-agent network, each agent is associated with a convex set. The objective is for all the agents to achieve an agreement within the intersection of the associated convex sets. A distributed"projected consensus algorithm" is employed, and the computation of the projection term is converted to a constrained optimization problem. The solution of the optimization problem is determined by Karush-Kuhn-Tucker(KKT) conditions. Some implementable algorithms based on the simplex method are introduced to solve the optimization problem. Two numerical examples are given to illustrate the effectiveness of the algorithms.     

The Alternative Property and Vector Optimization Problem in Ordered Locally Convex Topological Vector Spaces

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用于虚拟环境中实时避障的凸多边形融合算法

为了达到军事仿真中对智能体避障的实时性要求,我们提出了一种基于坐标变换的凸多边形融合算法。该算法包括了计算点到线段最小距离、判断线段与多边形是否相交、计算凸多边形之间近似距离以及获得融合点等内容。实验表明,将该算法应用于虚拟环境中智能体实时避障是可行和有效的。     

决策表的分布约简和严凸函数下约简的等价性

用严凸函数定义决策表的属性约简，证明用严凸函数定义的属性约简同分布约简是等价的，给出严凸函数定义的相对约简的一个判定定理。     

Lifts of Non-Compact Convex Sets and Cone Factorizations

Journal of Systems Science and Complexity - This paper generalizes the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, the...     

综合判断矩阵的几个性质

指出了一些文章关于判断矩阵凸组合和Hadamard凸组合一致性性质叙述中的几个小问题,在 已有证明方法的基础上给出了综合判断矩阵的几个性质,对群组决策具有较大的实用性.     

MODELLING RANDOM CONVEX SETS

A model is developed for convex-set valued data,which are the Minkowski sum of aconvex parameter set and a convex noise set.This model is generalized to include location and scaleparameters.A further generalization results in a model for convex sets which is analogous to aone-way analysis of variance models.In each case,estimators of the parameters are given which,under certain conditions,are shown to be consistent.Data generated from the model and theestimators are studied.An outlier detection method is examined.     

求解可分离连续凸二次背包问题的直接算法

经典算法一般采用迭代过程求解连续凸二次背包问题,研究了求解可分离连续凸二次背包问题的直接算法。分析了可分离连续凸二次背包问题的结构特性,通过两个命题和两个定理研究了可分离连续凸二次背包问题的解的特性,提出了一种快速的求解该问题的直接算法。该算法能快速有效地求解可分离连续凸二次背包问题的最优解,算法的时间复杂度和空间复杂度都是O(n),都比经典算法节约很多。