对LP问题有无穷多最优解判别定理证明的补充

本文指出了文献［１］中关于“无穷多最优解判别定理”证明中的不足，并给出了完整的证明     

On the Projections of Multivalued Maps

This paper considers analogues of the Helmholtz projections of the set of selections of a piecewise smooth multivalued map , n2. It is shown that, for mn–1 (m=1), the closure of the projection of on the subspace of gradient fields (solenoidal vector fields) is a convex set. For the general case, there are given point-wise conditions on the values of the map which ensure that the closure of the projection of contains the zero element. Possible applications to optimal control problems are discussed.     

Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

Bionomic exploitation of a ratio-dependent predator–prey system

The present article deals with the problem of combined harvesting of a Michaelis–Menten-type ratio-dependent predator–prey system. The problem of determining the optimal harvest policy is solved by invoking Pontryagin's Maximum Principle. Dynamic optimization of the harvest policy is studied by taking the combined harvest effort as a dynamic variable. Computer simulations are carried out to illustrate our analytical findings. Biological and bioeconomical interpretations of the results are explained critically.     

基于股价服从对数正态分布的凯利投资策略

基于集中投资策略的思想,把股票价格服从对数正态分布与凯利优化模型相结合,使其能更好地运用于股票投资实践中,推导出投资者个股投资的资产配置比例与投资者对个股投资收益率和标准差预测值之间的数学关系,从而实现最快财富增长速率的目标.     

The projected newton method for solving inverse eigenvalue problems - the case of multiple eigenvaues

This paper deals with the optimal solution of ill-posed linear problems, i.e..linear problems for which the solution operator is unbounded. We consider worst-case ar,and averagecase settings. Our main result is that algorithms having finite error (for a given setting) exist if and only if the solution operator is bounded (in that setting). In the worst-case setting, this means that there is no algorithm for solving ill-posed problems having finite error. In the average-case setting, this means that algorithms having finite error exist if and only lf the solution operator is bounded on the average. If the solution operator is bounded on the average, we find average-case optimal information of cardinality n and optimal algorithms using this information, and show that the average error of these algorithms tends to zero as n→∞. These results are then used to determine the [euro]-complexity, i.e., the minimal costof finding an [euro]-accurate approximation. In the worst-case setting, the [euro]comp1exity of an illposed problem is infinite for all [euro]>0; that is, we cannot find an approximation having finite error and finite cost. In the average-case setting, the [euro]-complexity of an ill-posed problem is infinite for all [euro]>0 iff the solution operator is not bounded on the average, moreover, if the the solutionoperator is bounded on the average, then the [euro]-complexity is finite for all [euro]>0.     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

求解两类Maxwell方程组棱元离散系统的快速算法和自适应方法

Maxwell方程组棱元离散系统的快速算法和自适应方法是当前计算电磁场中的研究热点和难点. 首先, 针对H(curl)椭圆方程组的棱元离散系统, 通过建立棱元空间的稳定性分解, 设计了相应的快速迭代法和高效预条件子, 并且证明了迭代算法的收敛率和预条件子的条件数均不依赖于模型参数和网格规模. 其次, 针对时谐Maxwell方程组的棱有限元方法, 利用离散的Helmholtz分解, 连续散度为零函数对离散散度为零函数的逼近性和对偶论证, 获得了在L²和H(curl)范数下的拟最优误差估计. 进而设计和分析了相应的两网格法. 最后, 分别针对变系数H(curl)椭圆方程组和不定时谐Maxwell方程组, 考虑了一种不需要标记振荡项和加密单元不需要满足“内节点” 性质的自适应棱有限元法(AEFEM), 并证明了AEFEM的收敛性. 进一步, 当初始网格和Dörfler标记策略参数满足一定的假设条件时, 利用AEFEM的收敛性、误差的整体下界和局部上界估计, 证明了AEFEM的拟最优复杂性.     

Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance

This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart. But the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter. This result is used to solve a kind of optimal portfolio choice problem and the optimal portfolio choice strategy is obtained. Computational results and figures explicitly illustrate the optimal solution and the sensitivity to the volatility rate parameter.     

A multi-objective mathematical model for the industrial hazardous waste location-routing problem

Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multi-objective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers; minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues; and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database.