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     

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.     

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.     

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。     

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.     

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 .     

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。     

THE RELATIONSHIP BETWEEN THE CONE-WEAK SUBDIFFERENTIAL AND CONE-WEAK DIRECTION DERIVATIVE FOR CONVEX SET-VALUED MAPPING

1.IntroductionInrecentyears,thetheoriesofgenerealdifferentialhaveplayedimportantrQleinthestudyanddevelopmelitofnonlinearfields(see[1-6])-Wehaveintroducedatypeofthecone-weaksubdfferentialofconvexset-valuedmappinginalocallyconvextopologicalvectorspacein[7-1l].ItdifferentsfromthosedefinedbyJ-P-Aubin,Ekeland,T.Tanino,Y.Sawaragi,B.S.Mordukhovichin[3-6].Ithasbeenusedtosolvetheoptimalproblemsofset-va-luedmaPpingssuchasthestabilityofoptimalsolutions,optimalconditions,dualtheorem,saddlepointstheo…     

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。     

平面点集凸壳的快速近似算法

提出并实现了平面点集凸壳的一种新的近似算法——多方向极值法。该算法首先根据用户输入的控制参数,顺序生成一系列极值方向,每个方向有对应的极值表达式;然后扫描平面点集中的点,依每个点的坐标更新各方向上的极值点信息;最后按照一定的顺序装配各极值点并去重,得到该平面点集的一个近似凸壳。实验表明,该算法执行效率高,不但可以单独应用在一些对时间要求比较苛刻而对精度要求不高的场合,而且可以作为快速凸壳算法的一个预处理过程。     

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.     

凸优化方法及其在排队系统中的应用研究

理论上可以证明严格凸优化问题有惟一的全局最优解；应用中有快速的多项式时间算法求解这一全局最优解。因此对难于解决的排队系统性能指标优化问题，如负荷配置问题．可以利用排队系统的凸性应用凸优化方法求解。本文基于排队理论建立排队系统负荷配置的非线性优化模型，设计一种优化变量转换方法并经适当的约束务件合并将该模型转换为凸优化模型．并引入凸优化内点法作为负荷配置的有效计算工具。实例计算结果表明．基于排队理论的非线性凸优化模型．其优化结果能保证充分利用设备的生产能力及最低的在制品库存；同时凸优化内点算法具有迭代次数少、收敛速度快的优点；涉及排队系统中其他性能指标的优化问题，也可以采用类似的方法求其最优解。     

不确定性离散时滞大系统的分散镇定控制

利用线性矩阵不等式方法研究了一类不确定离散大系统分散控制问题 ,且系统中具有时滞相关项。通过求解线性矩阵不等式 ,提出了系统可分散状态反馈镇定的充分条件 ,并给出了线性无记忆状态反馈分散控制器设计和优化方法。最后给出了数值算例以说明其可行性     

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.     

Cooperative games on convex geometries with a coalition structure

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure,which can be seen as an extension of cooperative games with a coalition structure.For this kind of games,the cooperation among unions and within each union will be the convex sets,i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively.The explicit form of the generalized Owen value for this kind of games is given,which can be seen as an extension of the Owen value.Furthermore,two special cases of this kind of games are researched.The corresponding payoff indices are also studied.Finally,an illustrative example is given.     

基于视觉的近距离编队对偶四元数相对位姿估计算法

针对近距离编队飞行中位姿估计问题,提出了一种新的点到区域匹配航天器间视觉相对位姿估计算法。给定主星表面上的点集及与之匹配的从星摄像机像平面图像凸区域,结合对偶四元数及凸优化数学工具,充分利用对偶四元数描述坐标系变换的简洁性,建立了对偶四元数凸优化位姿估计模型,估计出主星与从星之间的相对位姿参数。该算法不仅利用对偶四元数较传统四元数描述坐标系变换的优势,而且采用凸优化方法可大大降低传统位姿估计方法中需要精确的点到点匹配的要求。仿真结果证明,该算法能满足近距离编队相对位姿估计精度要求,具有较好的鲁棒性,对目前航天任务中航天器间视觉相对位姿估计具有重要参考价值。     

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

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针对目标跟踪的分布式MIMO雷达资源分配算法

基于分布式多输入多输出雷达,针对目标跟踪精度的优化问题提出了一种联合资源优化分配算法。首先,推导了机动目标跟踪误差的贝叶斯克拉美罗下界(Bayesian Cramer Rao lower bound, BCRLB),由BCRLB可知其跟踪精度主要由信号发射功率、带宽和信号有效时宽决定。然后,以最小化目标的BCRLB为目标函数,建立了包含相应的3个资源变量的优化模型,分析可知该模型的求解是一个非凸问题的求解。所以采用循环最小化算法和凸松弛的方法将这个非凸的优化模型转化为凸优化模型进行求解。最后,仿真结果表明,利用所提出的资源分配算法能明显提高机动目标的跟踪精度。     

Missile robust gain scheduling autopilot design using full block multipliers

Reduction of conservatism is one of the key and difficult problems in missile robust gain scheduling autopilot design based on multipliers. This article presents a scheme of adopting linear parameter-varying (LPV) control approach with full block multipliers to design a missile robust gain scheduling autopilot in order to eliminate conservatism. A model matching design structure with a high demand on matching precision is constructed based on the missile linear fractional transformation (LFT) model. By applying full block S-procedure and elimination lemma, a convex feasibility problem with an infinite number of constraints is formulated to satisfy robust quadratic performance specifications. Then a grid method is adopted to transform the infinite-dimensional convex feasibility problem into a solvable finite-dimensional convex feasibility problem, based on which a gain scheduling controller with linear fractional dependence on the flight Mach number and altitude is derived. Static and dynamic simulation results show the effectiveness and feasibility of the proposed scheme.     

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。