一种新的向量互补问题

本文在实局部凸空间中引入了一种新的向量互补问题,这一向量互补问题不仅包含了由Ｙｕ和Ｙａｏ提出的广义向量互补问题由Ｃｈｅｎ和Ｙａｎｇ定义的弱向量互补问题,而且还包含了Ｉｓａｃ意义下的隐互补问题。本文还讨论了新的向量互补问题,向量变分不等式,向量单向极小化问题和最小元问题之间的关系,给出了这一向量互补问题解的存在定理。     

下层独立的一主多从双层随机线性规划问题研究

Herminia I.Calvete等研究了一主多从双层确定性线性规划问题,证明了这类问题等价于一类常规的双层线性规划问题.本文在此基础上,推广确定型的问题到随机型优化情况,考虑了一类下层优化相互独立的一主多从双层随机优化问题(SLBMFP).在特定的随机变量分布条件下,理论上证明了该类问题可以转化为一主一从双层确定性优化问题.本文的研究对于求解一主多从双层随机优化模型,解决此类模型在实际应用中的问题具有一定的意义.     

A primal–dual algorithm for minimizing a sum of Euclidean norms

We study the problem of minimizing a sum of Euclidean norms. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. In this paper we first transform this problem and its dual problem into a system of strongly semismooth equations, and give some uniqueness theorems for this problem. We then present a primal–dual algorithm for this problem by solving this system of strongly semismooth equations. Preliminary numerical results are reported, which show that this primal–dual algorithm is very promising.     

Pendants-median支撑树及其一个相关问题:复杂性和算法

The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3).     

Using the parametric approach to solve the continuous-time linear fractional max–min problems

A numerical algorithm based on parametric approach is proposed in this paper to solve a class of continuous-time linear fractional max-min programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as a parametric continuous-time linear programming problem. We also introduce a dual problem of this parametric continuous-time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous-time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this algorithm.     

Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems

A Dinkelbach-type algorithm is proposed in this paper to solve a class of continuous-time linear fractional programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as parametric continuous-time linear programming problem. We also introduce a dual problem of this parametric continuous-time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous-time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this practical algorithm.     

About the Power Law of the PageRank Vector Component Distribution. Part 1. Numerical Methods for Finding the PageRank Vector

In Part 1 of this paper we consider the web-page ranking problem, also known as the problem of finding the PageRank vector, or the Google problem. We discuss the link between this problem and the ergodic theorem and describe different numerical methods to solve this problem together with their theoretical background, such asMarkov chain Monte Carlo and equilibrium in a macrosystem.     

移动通信系统中的最优功率控制算法

本文研究了移动通信系统中的功率最优控制问题.我们首先将这一个工程问题转化为最大可满足线性不等式组问题的一个特殊情形,然后通过对这个组合优化问题的最优解的性质研究,给出了求解该问题的多项式时间算法.     

一类亚半正定矩阵的左右逆特征值问题

1．引言在工程技术中常常遇到这样一类逆特征值问题：要求在一个矩阵集合S中，找具有给定的部分右特征对（特征值及相应的特征向量）和给定的部分左特征对（特征值及相应的特征向量）的矩阵．文［2］，［3］讨论了S为。x。实矩阵集合的情形．文［4］－［7］对S为nxn实对称矩阵．对称正定矩阵，对称半正定矩阵集合的情形进行了讨论．文【川讨论了S为亚正定阵集合的情形．并提到了对于亚半正定矩阵的情形目下无人涉及，有待进一步研究．本文将对S为nxn亚半正定矩阵集合的情形进行讨论．给出了亚半正定矩阵的左右逆特征值问题有解的充要条件…     

Numerical transformation methods: Blasius problem and its variants

Blasius problem is the simplest nonlinear boundary-layer problem. We hope that any approach developed for this epitome can be extended to more difficult hydrodynamics problems. With this motivation we review the so called Töpfer transformation, which allows us to find a non-iterative numerical solution of the Blasius problem by solving a related initial value problem and applying a scaling transformation. The applicability of a non-iterative transformation method to the Blasius problem is a consequence of its partial invariance with respect to a scaling group. Several problems in boundary-layer theory lack this kind of invariance and cannot be solved by non-iterative transformation methods. To overcome this drawback, we can modify the problem under study by introducing a numerical parameter, and require the invariance of the modified problem with respect to an extended scaling group involving this parameter. Then we apply initial value methods to the most recent developments involving variants and extensions of the Blasius problem.     

Polynomial Algorithms for a Class of Discrete Minmax Linear Programming Problems

We consider the problem of obtaining integer solutions to a minmax linear programming problem. Although this general problem is NP-complete, it is shown that a restricted version of this problem can be solved in polynomial time. For this restricted class of problems two polynomial time algorithms are suggested, one of which is strongly polynomial whenever its continuous analogue and an associated linear programming problem can be solved by a strongly polynomial algorithm. Our algorithms can also be used to obtain integer solutions for the minmax transportation problem with an inequality budget constraint. The equality constrained version of this problem is shown to be NP-complete. We also provide some new insights into the solution procedures for the continuous minmax linear programming problem.     

Iterative approximation of a common solution of a split equilibrium problem,a variational inequality problem and a fixed point problem

In this paper, we introduce an iterative method to approximate a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in real Hilbert spaces. We prove that the sequences generated by the iterative scheme converge strongly to a common solution of the split equilibrium problem, the variational inequality problem and the fixed point problem for a nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area.     

Problem difficulty of real instances of convoy planning

Moving men and materials in large numbers and quantities is a long-standing military problem faced by all arms. An important part of this is the routing of convoys so that they reach their correct destinations in the shortest time. The optimization problem at the heart of this problem is referred to as the convoy movement problem. Previous work on the convoy movement problem has made the assumption that the problem is difficult in practice because of the NP-hardness of the problem in combination with the limited success of early approaches based on genetic algorithms. As a result subsequent work has focused on mathematical programming-based methods, principally Lagrangian relaxation. In this paper, we demonstrate that a straightforward reformulation of the problem renders the real-world like instances, used to benchmark previous approaches, amenable to solution by simple heuristics. The main lessons learnt from this work is that analysis of the problem in conjunction with simple algorithms can, in practice, yield surprisingly effective solutions.     

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。     

General fractional variational problem depending on indefinite integrals

In this report, we consider two kind of general fractional variational problem depending on indefinite integrals include unconstrained problem and isoperimetric problem. These problems can have multiple dependent variables, multiorder fractional derivatives, multiorder integral derivatives and boundary conditions. For both problems, we obtain the Euler-Lagrange type necessary conditions which must be satisfied for the given functional to be extremum. Also, we apply the Rayleigh-Ritz method for solving the unconstrained general fractional variational problem depending on indefinite integrals. By this method, the given problem is reduced to the problem for solving a system of algebraic equations using shifted Legendre polynomials basis functions. An approximate solution for this problem is obtained by solving the system. We discuss the analytic convergence of this method and finally by some examples will be showing the accurately and applicability for this technique.     

Fixed-Point Technique for Implicit Complementarity Problem in Hilbert Lattice

In this paper, we consider and study the implicit complementarity problem in the setting of a Hilbert lattice. It has been shown that this problem can be formulated as a fixed-point problem by using a suitable change of variables. Moreover, this formulation allows us to prove the existence and uniqueness of solutions of the implicit complementarity problem.     

A branch and bound network approach to the canonical constrained entropy problem

In this paper, we present a branch and bound algorithm for solving the constrained entropy mathematical programming problem. Unlike other methods for solving this problem, our method solves more general problems with inequality constraints. The advantage of the proposed technique is that the relaxed problem solved at each node is a singly constrained network problem. The disadvantage is that the relaxed problem has twice as many variables as the original problem. An application to regional planning is given, and an example problem is solved.     

A New Pareto Optimal Solution in a Lagrange Decomposable Multi-Objective Optimization Problem

In this paper a committee decision-making process of a convex Lagrange decomposable multi-objective optimization problem, which has been decomposed into various subproblems, is studied. Each member of the committee controls only one subproblem and attempts to select the optimal solution of this subproblem most desirable to him, under the assumption that all the constraints of the total problem are satisfied. This procedure leads to a new solution concept of a Lagrange decomposable multi-objective optimization problem, called a preferred equilibrium set. A preferred equilibrium point of a problem, for a committee, may or may not be a Pareto optimal point of this problem. In some cases, a non-Pareto optimal preferred equilibrium point of a problem, for a committee, can be considered as a special type of Pareto optimal point of this problem. This fact leads to a generalization of the Pareto optimality concept in a problem.     

一类广义半无限规划问题的一阶最优性条件

本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题。在一定的条件下将其转化为标准的半无限极小极大规划问题。研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件。     

Bin covering algorithms in the second stage of the lot to order matching problem

We formulate the problem of effectively assigning semiconductor fabrication wafer lots to customer orders of various sizes, or the lot-to-order matching problem, as an integer programming problem. Our goal in this paper is to develop an efficient, practical method for solving this problem for various performance measures. Because of its complexity we decompose the problem into a knapsack problem coupled with a generalized bin-covering problem, and solve these subproblems sequentially using heuristic methods. We restrict our attention to solution methods for the less-common second subproblem, and analyze the performance of several heuristics using a data set representative of real situations in a semiconductor back-end. Based on this analysis, we show that these heuristics perform significantly better than current industrial practice in the context of the overall problem.