含弹性约束的多目标模糊线性规划求解

本文讨论了一类含弹性约束的多目标模糊线性规划问题.利用模糊结构元方法引入模糊数的加权特征数概念和序关系,应用Verdegay的模糊线性规划方法及模糊数的加权特征数将此类多目标模糊线性规划问题转化成一类含参数约束条件的清晰多目标线性规划模型,并应用一种基于线性加权函数的规划算法求其α-拟最优可行解.最后,给出了一个数值实例来说明如何求解此类多目标模糊线性规划问题.     

带新NCP函数的Lagrangian乘子方法

在经营管理、工程设计、科学研究、军事指挥等方面普遍存在着最优化问题,而实际问题中出现的绝大多数问题都被归纳为非线性规划问题之中。作为带等式、不等式约束的复杂事例,最优化问题的求解向来较为繁琐、困难。适当条件下,非线性互补函数(NCP)可以与约束优化问题相结合,其中NCP函数的无约束极小解对应原约束问题的解及其乘子。本文提出了一类新的NCP函数用于解决等式和不等式约束非线性规划问题,结合新的NCP函数构造了增广Lagrangian函数。在适当假设条件下,证明了增广Lagrangian函数与原问题的解之间的一一对应关系。同时构造了相应算法,并证明了该算法的收敛性和有效性。     

全局求解线性多乘积规划的分支定界算法

本文针对一类线性多乘积规划问题提出一种分支定界算法.首先将原问题转化为其等价形式,然后利用提出的线性松弛技术将等价问题松弛为线性规划问题,通过求解一系列线性规划问题得到原问题的全局最优解.最后给出算法的收敛性和计算复杂性.数值实验表明算法是有效的.     

含直觉模糊弹性约束的多目标模糊线性规划求解

基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的多目标模糊线性规划问题.通过引入模糊数的加权特征数,定义了一种序关系并拓展了Verdegay的模糊线性规划方法,将上述多目标模糊线性规划问题转化成两个等价含参数约束条件的清晰多目标线性规划模型,并应用一种线性加权函数法给出了此类线性规划模型的对比最优可行解.最后通过一个数值实例来说明此类问题的一般求解方法.     

求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.     

一类全局优化问题的线性化方法

本文对带有不定二次约束且目标函数为非凸二次函数的最优化问题提出了一类新的确定型全局优化算法,通过对目标函数和约束函数的线性下界估计,建立了原规划的松弛线性规划,通过对松弛线性规划可行域的细分以及一系列松弛线性规划的求解过程,得到原问题的全局最优解.我们从理论上证明了算法能收敛到原问题的全局最优解.     

分片线性NCP函数滤子QP-free算法

本文定义了分片线性NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.利用优化问题的一阶KKT条件,乘子和NCP函数,得到对应的非光滑方程组.本文给出解这非光滑方程组算法,它包含原始-对偶变量,在局部意义下,可看成关扰动牛顿-拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,在适当假设下算法具有超线性收敛性.     

大规模非线性互补问题的共轭梯度法

提出求解大规模非线性互补问题NCP(F)的PRP型共轭梯度法,算法自然满足充分下降条件.当F是可微P_0+R_0函数且F'(χ)在水平集上全局Lipschitz连续条件下,证明了算法的全局收敛性.数值结果表明算法的有效性.     

求解摩擦接触问题的一个非内点光滑化算法

给出了一个求解三维弹性有摩擦接触问题的新算法,即基于NCP函数的非内点光滑化算法．首先通过参变量变分原理和参数二次规划法,将三维弹性有摩擦接触问题的分析归结为线性互补问题的求解;然后利用NCP函数,将互补问题的求解转换为非光滑方程组的求解;再用凝聚函数对其进行光滑化,最后用NEWTON法解所得到的光滑非线性方程组．方法具有易于理解及实现方便等特点．通过线性互补问题的数值算例及接触问题实例证实了该算法的可靠性与有效性．     

一个求解水平线性互补问题的高阶可行内点算法的多项式复杂性

最近,Zhao和Sun提出了一个求解sufficient线性互补问题的高阶不可行内点算法.不需要严格互补解条件,他们的算法获得了高阶局部收敛率,但他们的文章没有报告多项式复杂性结果.本文我们考虑他们所给算法的一个简化版本,即考虑求解单调水平线性互补问题的一个高阶可行内点算法.我们证明了算法的迭代复杂性是     

Fast elliptic curve point multiplication based on binary and binary non-adjacent scalar form methods

This article presents two methods for developing algorithms of computing scalar multiplication in groups of points on an elliptic curve over finite fields. Two new effective algorithms have been presented: one of them is based on a binary Non-Adjacent Form of scalar representation and another one on a binary of scalar representation method. All algorithms were developed based on simple and composite operations with point and also based on affine and Jacobi coordinates systems taking into account the latest achievements in computing cost reduction. Theorems concerning their computational complexity are formulated and proved for these new algorithms. In the end of this article comparative analysis of both new algorithms among themselves and previously known algorithms are represented.     

An experimental evaluation of the efficacy of four multi-objective linear programming algorithms

Four multi-objective linear programming algorithms are implemented on microcomputer software packages and a large field experiment is conducted using the implemented algorithms. Two new algorithms which incorporate formal models of decision maker behavior are tested along with two established algorithms which include no formal models of decision maker behavior. The new algorithms are shown to outperform the established algorithms.     

基于中心路径大邻域上的一类非单调线性互补问题的高阶可行内点算法

In this paper a high-order feasible interior point algorithm for a class of nonmonotonic (P-matrix) linear complementary problem based on large neighborhoods of central path is presented and its iteration complexity is discussed.These algorithms are implicitly associated with a large neighborhood whose size may depend on the dimension of the problems. The complexity of these algorithms bound depends on the size of the neighborhood. It is well known that the complexity of large-step algorithms is greater than that of short- step ones. By using high-order power series (hence the name high-order algorithms), the iteration complexity can be reduced. We show that the upper bound of complexity for our high-order algorithms is equal to that for short-step algorithms.     

特征向量计算的神经网络方法

矩阵特征向量计算在实际问题中有着广泛应用，本文采用神经网络计算方法来研究主元分析（ＰＣＡ）和次元分析（ＭＣＡ）问题．我们首先考虑神经元的情况（ｐ＝１），给出了求矩阵最大特征元和最小特征元的算法。然后对多神经元性形（ｐ〉１），给出了抽取矩阵主元和次元的算法．和目前许多元知的算法不一样，在我们ＰＣＡ的算法中发迹矩阵的负号就能够得到ＭＣＡ问题的解。     

Homogeneous algorithms for multiextremal optimization

The class of homogeneous algorithms for multiextremal optimization is defined, and a number of theorems are proved, including a sufficient condition for the convergence of homogeneous algorithms to a global minimizer. An approach to the synthesis of homogeneous algorithms based on model multi-peak functions is proposed. The existing algorithms are reviewed, and a new efficient multidimensional algorithm based on the Delaunay triangulation is constructed. Some numerical results are presented.     

论并行算法的分类

§1.引言利用并行计算系统求解数值计算问题或非数值计算问题,需根据系统的类型设计并行算法。自然,并行算法设计的主要基础是求解问题所涉及的学科领域中的原理和方法,或直接揭示某些已有方法中潜在的并行性,或推广某些原理发展显含并行性的新方法。但是,要建立可行(能在一个并行计算系统中实现)和有效(能充分发挥系统性能使并行度与     

Hybridizing local search algorithms for global optimization

In this paper, we combine two types of local search algorithms for global optimization of continuous functions. In the literature, most of the hybrid algorithms are produced by combination of a global optimization algorithm with a local search algorithm and the local search is used to improve the solution quality, not to explore the search space to find independently the global optimum. The focus of this research is on some simple and efficient hybrid algorithms by combining the Nelder–Mead simplex (NM) variants and the bidirectional random optimization (BRO) methods for optimization of continuous functions. The NM explores the whole search space to find some promising areas and then the BRO local search is entered to exploit optimal solution as accurately as possible. Also a new strategy for shrinkage stage borrowed from differential evolution (DE) is incorporated in the NM variants. To examine the efficiency of proposed algorithms, those are evaluated by 25 benchmark functions designed for the special session on real-parameter optimization of CEC2005. A comparison study between the hybrid algorithms and some DE algorithms and non-parametric analysis of obtained results demonstrate that the proposed algorithms outperform most of other algorithms and their difference in most cases is statistically considerable. In a later part of the comparative experiments, a comparison of the proposed algorithms with some other evolutionary algorithms reported in the CEC2005 confirms a better performance of our proposed algorithms.     

Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix.     

A comparison of sequential Delaunay triangulation algorithms

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm.

Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.     

A new iterative Monte Carlo approach for inverse matrix problem

A new approach of iterative Monte Carlo algorithms for the well-known inverse matrix problem is presented and studied. The algorithms are based on a special techniques of iteration parameter choice, which allows to control the convergence of the algorithm for any column (row) of the matrix using different relaxation parameters. The choice of these parameters is controlled by a posteriori criteria for every Monte Carlo iteration. The presented Monte Carlo algorithms are implemented on a SUN Sparkstation. Numerical tests are performed for matrices of moderate in order to show how work the algorithms. The algorithms under consideration are well parallelized.