离散设施选址问题研究综述

本文首先回顾了设施选址问题百年发展历史,认为其研究经历了零散研究、系统研究、不确定性研究三个阶段.离散选址问题包括中值问题、覆盖问题、中心问题、多产品问题、动态问题、多目标问题、路径选址问题、网络中心选址问题8个子问题.最后作者讨论了选址问题研究中存在的问题以及今后发展的趋势.     

一类非单调互补问题的Canonical对偶问题研究

对于一类具有广泛应用背景的非单调互补问题,我们构建了这类问题的Canonical对偶问题。其对偶问题可以写成和原问题类似的互补问题。我们给出了对偶问题和原问题解之间的对偶关系,并且将对偶问题转化成一个一维优化问题,这不但可以方便的求解这类问题,也为研究这类问题性质提供了一个非常直观的研究工具。最后,本文给出了几个算例来演示对偶问题的性质。     

运输问题悖论及其研究

提出了运输问题的奇特现象——运输问题的悖论,讨论了运输问题悖论出现的条件,最后指出了研究运输问题悖论的现实意义.     

基于遗传算法的大学课程表问题研究

课程表问题是时间表问题之一 ,也是 NP难问题 .根据大学授课形式的特点建立了大学课程表问题的数学模型 ,给出了求解该问题的遗传算法 .根据模型和大学课程表问题的特点设计了一种全新的编码 ,提出了一种新形式的交叉方式 .实验结果表明该方法是可行和有效的 .     

半凸多目标优化ε-拟弱有效解的最优性条件及对偶定理

本文在相关文献考虑MP问题的基础上,增加了等式约束条件,即本文考虑了VP问题,并将已有文献中的凸性假设改为半凸性假设,得到VP问题的ε-拟弱有效解的相应最优性条件.接着,本文定义了VP问题的拉格朗日函数及其ε-拟弱鞍点,得到VP问题的ε-拟弱鞍点相应定理.最后,本文考虑了VP问题的对偶问题,获得了VP问题的弱对偶和强对偶定理.     

运筹学中几种运输问题的求解方法探析

从目前研究生入学考试中出现的几种新的运筹学运输问题出发,探讨了各种运输问题与传统运输问题的差异。提出以传统运输问题为本,将非传统运输问题转化为传统运输问题借助表上作业法求解的思路。并针对6种不同的非传统运输问题分析了转化的过程和步骤,为运输问题的研究提供了新的内容.     

货运列车的优化编组调度方案与实现方法

针对2008年全国研究生数学建模竞赛C题"货运列车的编组调度问题",首先介绍了问题的背景和问题的构成,并提出了6个要解决的问题;然后概要地分析介绍了解决这6个具体问题的思想方法;接着给出了具体解决问题的实现方法、主要模型和求解思路;最后对参赛队的总体做法和存在问题情况做了较详细的分析,并就与这个题目有关的几个问题做了说明.     

椭圆型变分不等式的障碍优化控制问题

讨论了椭圆型变分不等式的障碍优化控制问题,获得了优化控制问题的解的存在性、唯一性和相关问题的正则性等,并研究了优化控制问题的逼近等．     

隐式形式多值向量均衡问题解的存在性

考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果.     

伪单调型向量F-互补问题可行集的最小元问题

本文引入了几类向量F-互补问题并给出了向量F-互补问题与广义向量变分不等式之间的关系.通过定义向量F-互补问题的可行集,研究了伪单调型向量F-互补问题的可行集的最小问题,推广了已有的一些结果.     

Parametric network utility maximization problem

We show how to solve the parametric utility maximization problem with a continuous parameter in a finite number of steps in order to obtain a solution with given accuracy. Also, we propose a new approach for the discretization of time for the parametric utility maximization problem with Lipschitz utility function. Some numerical results are provided.     

Stochastic utilities with subsistence and satiation: Optimal life insurance purchase,consumption and investment

We introduce stochastic utilities such that utility of any fixed amount of interest is a stochastic process or random variable. Also, there exist stochastic (or random) subsistence and satiation levels associated with stochastic utilities. Then, we consider optimal consumption, life insurance purchase and investment strategies to maximize the expected utility of consumption, bequest and pension with respect to stochastic utilities. We use the martingale approach to solve the optimization problem in two steps. First, we solve the optimization problem with an equality constraint which requires that the present value of consumption, bequest and pension is equal to the present value of initial wealth and income stream. Second, if the optimization problem is feasible, we obtain the explicit representations of the replicating life insurance purchase and portfolio strategies. As an application of our general results, we consider a family of stochastic utilities which have hyperbolic absolute risk aversion (HARA).     

Portfolio selection under incomplete information

We study an optimal investment problem under incomplete information and power utility. We analytically solve the Bellman equation, and identify the optimal portfolio policy. Moreover, we compare the solution to the value function in the fully observable case, and quantify the loss of utility due to incomplete information.     

Funding and investment decisions in a stochastic defined benefit pension plan with regime switching*

In this paper, we consider a continuous-time Markov regime-switching model for a pension plan with a collective defined benefit character. In particular, we focus on optimal funding and asset allocation problem for a fund manager who wants to maximize the expected utility of the difference ratio between the benefit and contribution rates to the total salary until ruin. Using the techniques and methods of stochastic control, we present a system of Hamilton–Jacobi–Bellman equations for this optimization problem and establish a verification theorem. In the special cases of logarithmic and power utility, we solve the problem explicitly and present some numerical examples to illustrate our results.     

考虑群体一致性的动态群体决策方法

为了求解一类包含多轮群体评价过程的动态群体决策问题，定义了个体效用波动和群体一致度的概念并分别建立了相应的计算指标，利用决策个体的效用波动指标提出了决策个体权重的修正方法，然后提出了一种基于群体一致度指标的加权算法，得到了各决策方案的群体效用评价。最后给出了计算实例。     

Optimal Control for Utility Portfolio Selection with Liability

In this paper we use stochastic optimal control theory to investigate a dynamic portfolio selection problem with liability process, in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices. We apply dynamic programming principle to obtain Hamilton-Jacobi-Bellman (HJB) equations for the value function and systematically study the optimal investment strategies for power utility, exponential utility and logarithm utility. Firstly, the explicit expressions of the optimal portfolios for power utility and exponential utility are obtained by applying variable change technique to solve corresponding HJB equations. Secondly, we apply Legendre transform and dual approach to derive the optimal portfolio for logarithm utility. Finally, numerical examples are given to illustrate the results obtained and analyze the effects of the market parameters on the optimal portfolios.     

多周期公用工程系统运行的模型,优化方法与应用

针对多周期公用工程系统的运行优化问题，考虑了设备的启停费用的情况下。建立了混合整数非线性规划模型并证明了最优解的存在性。针对该运行优化问题本将其分解成若干子问题，然后利用改进的Hooke-Jeeves优化算法求解每个子问题。应用于具体实例，其数值结果与其它方法得到的相比。运行时间短，且更适合多周期公用工程问题的求解。     

Dynamic convex duality in constrained utility maximization

ABSTRACT

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of forward and backward stochastic differential equations (FBSDEs) plus some additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. We also find that the optimal wealth process coincides with the adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems, which contrasts the simplicity of the duality approach we propose and the technical complexity of solving the primal problem directly.     

Optimal Compensation with Hidden Action and Lump-Sum Payment in a Continuous-Time Model

We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions. The optimal contract is, in general, a nonlinear function of the final outcome only, while in the previously solved cases, for exponential and linear utility functions, the optimal contract is linear in the final output value. In a specific example we compute, the first-best principal’s utility is infinite, while it becomes finite with hidden action, which is increasing in value of the output. In the second part of the paper we formulate a general mathematical theory for the problem. We apply the stochastic maximum principle to give necessary conditions for optimal contracts. Sufficient conditions are hard to establish, but we suggest a way to check sufficiency using non-convex optimization.     

指数效用函数下投资组合问题的有效集方法

本在指数型效用函数条件下提出了求解高维数组合投资问题的有效集方法，实例说明：该方法是可行的、有效的．