非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

相对非扩张映射和均衡问题的投影迭代算法

本文利用广义f-投影,在Banach空间中,建立求解相对非扩张映射不动点集合和均衡问题解集的公共元素的迭代算法.在适当条件下,我们也得到关于相对非扩张映射和均衡问题的强收敛性定理.     

互补约束均衡优化的一个共轭梯度投影法

讨论均衡约束最优化问题,利用一个互补函数和扰动技术将原问题转换为非线性等式约束最优化问题,然后利用共轭梯度投影算法的思想,给出了问题的一个求解算法,在适当的条件下,证明了算法的全局收敛性.     

鞍点问题的一种新的SOR迭代法（英文）

鞍点问题广泛出现在科学计算和工程应用的许多领域中,对这类线性系统的数值解法的研究已成为近年来的一个热点.基于鞍点问题系数矩阵的一个一般性的分裂,我们提出一种新的SOR迭代法,该方法是之前有关方法的推广和延伸.我们在一定的条件下讨论新方法的收敛性,数值实验表明该方法是有效的.     

具有控制结构的集值强向量均衡问题的稳定性

研究了具有控制结构的集值强向量均衡问题.通过Ky Fan截口定理得到了具有控制结构的集值强向量均衡问题解的存在性定理.并在映射满足一定条件的基础上,得到了集值强向量均衡问题所构成的空间M中,大多数(在Baire分类意义下)强向量均衡问题解集是稳定的.     

抽象经济均衡问题解的存在性及其算法

本文首先研究一类新的向量均衡问题,利用截口定理与KKM定理两种不同的工具证明此类均衡问题解的存在性,接着,把这类向量均衡问题推广到更为一般的情形,随后讨论了具有上下界的均衡问题,它是由Isac,Sehgal和Singh于1999年提出的一个公开问题,本文在一定条件下获得了一个新的解的存在性定理,并构造了一个迭代算法,讨论了算法的收敛性。     

互补约束规划问题的一个广义梯度投影算法

本文研究了一类均衡约束最优化问题.利用广义梯度投影法,结合罚函数思想,得到了一个初始点可以任意的广义梯度投影算法.在较弱的条件下,证明了算法的全局收敛性.     

强向量均衡问题与不动点问题的粘性逼近算法

讨论了强向量均衡问题与非扩张映射不动点问题的公共解.首先,给出了强向量均衡问题的辅助问题,并在适当的条件下,证明了其解的存在性和唯一性结果.然后,利用这些结果,提出了强向量均衡问题与非扩张映射不动点问题公共解的粘性逼近算法,并进一步证明了,在适当的条件下,由该算法产生的迭代序列强收敛于强向量均衡问题和非扩张映射不动点问题的公共解.     

线性均衡约束最优化的一个广义投影强次可行方向法

本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.     

均衡度公理化定义的改进

研究均衡度概念的公理化定义及其构造问题.首先,借助实例说明现有均衡度定义存在的问题;随后,在分析均衡度概念的特点和典型均衡度函数的图形的基础上,给出一种新的均衡度公理化定义.接着,讨论均衡度函数的构造问题,给出四类常用的均衡度函数,证明了均衡度函数与一类单调函数的复合仍是均衡度.最后,讨论了新的均衡度定义与原定义之间的关系以及四类常见均衡度函数之间的关系.     

一类多值多导数方法的收敛性与稳定性

1 引言 对于多值多导数方法,由于其多值多导的结构特点有利于提高解的精度,以及其包容性大,它包含了当今常用的多种常微数值方法,诸如:线性多步法,单支方法,多步多导方法,多(单)步Runge—Kutta方法,多导Runge-Kutta方法以及混合方法等.因此收敛性与稳定性的研究具有重要的实践意义和广泛的理论指导意义,也正因如此,这方面的研究工作引起了众多数值工作者们的兴趣,近年来,多值多导法求解刚性问题的B—收敛及其非线性稳定性的研究工作巳获得较大进展,其相应成果可参见文献[1—3],在文献[4,5]中笔者则针对Banach空间中一类非刚性问题-K~((p))类问题,分别探讨了多步多导法及单支方法的收敛性     

The -digraph optimization problem and the greedy algorithm

In this paper we present a new optimization problem and a general class of objective functions for this problem. We show that optimal solutions to this problem with these objective functions are found with a simple greedy algorithm. Special cases include matroids, Huffman's data compression problem, a special class of greedoids, a special class of min cost max flow problems (related to Monge sequences), a special class of weighted f-factor problems, and some new problems.     

一般形式的一阶椭圆型偏微分方程组拟线性Riemann-Hilbert问题

在文［ｌ，２，３］中，Ｅ．Ｗｅｇｅｒｔ和Ｌ．Ｖ．Ｗｏｌｆｅｒｓｄｏｒｆ等人讨论了一类全纯函数的拟线性Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ 问题在 Ｈａｒｄｙ空间中的可解性，在文［４］中，讨论了广义解析函数的拟线性 Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题，同样得到该边值问题在Ｈ２类解空间中的可解性、本文在前面研究工作的基础上，对一般形式的一阶椭圆型偏微分方程组拟线性Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题作了更深入的讨论，在适当的假设条件下，应用积分算子理论，函数论方法及不动点原理，证明了该边值问题在相应的泛函空间中同样是可解的．     

Decision Problems in Quadratic Function Fields of High Genus

This paper provides verification procedures for a number of decision problems in quadratic function fields of odd characteristic, thereby establishing membership of these problems in both NP and co-NP. The problems include determining the ideal and divisor class numbers of the field, the regulator of the field (in the real case), a generating system of the ideal class group, a basis of the ideal class group, the pricipality of an ideal, the equivalence of two ideals, the discrete logarithm of an ideal class with respect to another ideal class, and the order of a class in the ideal class group. While several of these problems belong to the aforementioned complexity classes unconditionally, others require a certain assumption to ensure that the verification procedures can be done in polynomial time; so far, this assumption has only been verified for fields of high genus.     

一类特殊多项式整数规划问题的最优化算法

本文考虑了一类特殊的多项式整数规划问题。此类问题有很广泛的实际应用,并且是NP难问题。对于这类问题,最优性必要条件和最优性充分条件已经给出。我们在本文中将要利用这些最优性条件设计最优化算法。首 先,利用最优性必要条件,我们给出了一种新的局部优化算法。进而我们结合最优性充分条件、新的局部优化算法和辅助函数,设计了新的全局最优化算法。本文给出的算例展示出我们的算法是有效的和可靠的。     

一类非线性演化方程初值问题的幂级数解

研究了一类非线性演化方程初值问题.通过不变子空间方法,这类初值问题被约化为常微分方程组的初值问题.这类初值问题是适定的.本文给出了这类初值问题关于时间变量t的幂级数解.     

A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems

Recently, the study of symmetric cone complementarity problems has been a hot topic in the literature. Many numerical methods have been proposed for solving such a class of problems. Among them, the problems concerned are generally monotonic. In this paper, we consider symmetric cone linear complementarity problems with a class of non-monotonic transformations. A smoothing Newton algorithm is extended to solve this class of non-monotonic symmetric cone linear complementarity problems; and the algorithm is proved to be well-defined. In particular, we show that the algorithm is globally and locally quadratically convergent under mild assumptions. The preliminary numerical results are also reported.     

A note on scheduling alternative operations in two-machine flowshops

In this note, we consider a class of problems for scheduling a set of jobs each of which consists of two consecutive operations. The jobs are to be processed in a two-machine flowshop in which either or both machines are versatile. A versatile machine can perform both operations of a job. The objective is to minimise the makespan. While the whole class of problems has been shown to be NP-complete, we provide a general pseudopolynomial dynamic programming scheme which solves the problems analytically. This also establishes that the problems are only NP-complete in the ordinary sense. The solution scheme can be modified to solve another class of similar two-machine flowshop scheduling problems.     

On proximal gradient method for the convex problems regularized with the group reproducing kernel norm

We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping, regularized by the group reproducing kernel norm. This class of problems arise naturally from applications in group Lasso, which is a popular technique for variable selection. An effective approach to solve such problems is by the proximal gradient method. In this paper we derive and study theoretically the efficient algorithms for the class of the convex problems, analyze the convergence of the algorithm and its subalgorithm.     

Hidden Convex Minimization

A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation.