关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.     

A numerical method for an optimal control problem with minimum sensitivity on coefficient variation

In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method.     

Simultaneous Optimal Controls for Non-Stationary Stokes Systems

This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented.     

复合二项对偶模型的最优分红问题

研究复合二项对偶模型的最优分红问题,通过分析HJB方程得到了最优分红策略和相应的最优值函数之间的关系以及最优值函数的简单计算方法.通过讨论最优红利策略的一些性质得到了最优值函数的可无限逼近的上界和下界.     

An optimal homotopy analysis method based on particle swarm optimization: application to fractional-order differential equation

This paper describes a new problem-solving mentality of finding optimal parameters in optimal homotopy analysis method (optimal HAM). We use particle swarm optimization (PSO) to minimize the exact square residual error in optimal HAM. All optimal convergence-control parameters can be found concurrently. This method can deal with optimal HAM which has finite convergence-control parameters. Two nonlinear fractional-order differential equations are given to illustrate the proposed algorithm. The comparison reveals that optimal HAM combined with PSO is effective and reliable. Meanwhile, we give a sufficient condition for convergence of the optimal HAM for solving fractional-order equation, and try to put forward a new calculation method for the residual error.     

Sensitivity analysis of the optimal assignment

This paper concentrates on sensitivity analysis of the optimal solution for the assignment problem (AP). Due to the high degeneracy of the AP, traditional sensitivity analysis, which determines the range in which the current optimal basis remains optimal, is impractical. Thus, changing the optimal basis does not ensure that the optimal assignment will be changed. Herein we investigate the properties of the AP and then propose several lemmas to determine two other types of sensitivity range. The first type is used to determine the range in which the current optimal assignment remains optimal. We further discuss what is the new optimal assignment when the changes surpass the range. The second type of sensitivity range is to determine those values of assignment model parameters for which the rate of change of optimal value function remains constant. An example is presented in order to demonstrate that the approaches are useful in practice.     

Limiting behavior of bang-bang controls for Sobolev problems

We consider the limiting behavior of optimal bang-bang controls as a family of Sobolev equations formally converges to a wave equation. The weak-starlimit of the sequence of bang-bang controls is an optimal control for the wave equation problem. The associated optimal states converge strongly and, for the optimal time problem, the optimal times converge to the optimal time for the wave equation.This work was supported in part by the National Science Foundation, Grant No. MCS-79-02037.     

Enumeration of All Possibly Optimal Vertices with Possible Optimality Degrees in Linear Programming Problems with a Possibilistic Objective Function

In this paper, we treat linear programming problems with fuzzy objective function coefficients. To such a problem, the possibly optimal solution set is defined as a fuzzy set. It is shown that any possibly optimal solution can be represented by a convex combination of possibly optimal vertices. A method to enumerate all possibly optimal vertices with their membership degrees is developed. It is shown that, given a possibly optimal extreme point with a higher membership degree, the membership degree of an adjacent extreme point is calculated by solving a linear programming problem and that all possibly optimal vertices are enumerated sequentially by tracing adjacent possibly optimal extreme points from a possibly optimal extreme point with the highest membership degree.     

基于腐损程度的季节性产品动态定价与订单量的集成优化

为了对易腐季节性产品的销售价格和订单量进行最优决策,考虑产品在不同腐损程度的情形下,需求与价格和时间同时相关的一类季节性产品的动态定价和订单量的集成优化问题.建立该类产品的价格制订次数、每次制订的价格和订单量的集成优化模型,并对模型进行求解,最后结合数例验证模型的实用性和可操作性,并分析产品腐损程度对价格制订次数、价格大小、订单量和利润的影响.结果表明,随着产品腐损程度的提高,零售商在销售季节内的产品价格最优制订次数保持不变;零售商在销售季节内所制订的最优价格逐渐微降;产品的最优订单量和所产生的最优利润逐渐微升.     

Strongly optimal algorithms and optimal information in estimation problems

This paper studies some aspects of information-based complexity theory applied to estimation, identification, and prediction problems. Particular emphasis is given to constructive aspects of optimal algorithms and optimal information, taking into account the characteristics of certain types of problems. Special attention is devoted to the investigation of strongly optimal algorithms and optimal information in the linear case. Two main results are obtained for the class of problems considered. First, central algorithms are proved to be strongly optimal. Second, a simple solution is given to a particular case of optimal information, called optimal sampling design, which is of great interest in system and identification theory.     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

Nonlinear optimal feedback control for lunar module soft landing

In this paper, the task of achieving the soft landing of a lunar module such that the fuel consumption and the flight time are minimized is formulated as an optimal control problem. The motion of the lunar module is described in a three dimensional coordinate system. We obtain the form of the optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results show that the proposed approach is highly effective.     

冲裁件有约束最优剪切方式的设计

本文讨论冲裁件有约束最优剪切方式的设计问题 .阐明最优剪切排样方式的规范结构 ;采用分支定界法求解冲裁件无约束排样问题 ;将有约束排样问题转换为求解一系列的无约束排样问题 ,并通过对解的性质分析提高算法效率 .实验计算结果说明本文算法十分有效 .最后给出一例题的最优排样方式 .     

Finding the optimum domain of a nonlinear wave optimal control system by measures

We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given.     

一类非平稳随机传递系统的最佳非线性滤波及优化算法

运用最佳非线性滤波方法及优化算法,讨论了一类不完全数据与具有连续时间的非平稳随机过程的最佳控制问题,得到了这两种状态下的两个最佳控制数学模型,给出了这类非平稳随机传递系统的最佳编码与最佳译码的建立方法,为解决这类非平稳随机过程的最佳控制提供了一种有效可靠的解决方法.     

供应中断下具有随机需求的闭环供应链最优差别定价模型

研究了在供应中断下具有随机需求的闭环供应链系统的最优差别定价模型.基于博弈论的理论和方法分别在集中式和分散式决策情形下,确定了最优批发价、最优销售价、最优订购量及系统利润.最后通过数值例子对最优差别定价模型进行了实证分析.     

Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem

We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.     

三参数线性规划最优基的稳定性分析

在这篇文章里我们研究一种含三个参数的线性规划最优基的稳定性.得出了最优基的稳定性及二维稳定性的一些较好的结果和最优基稳定的充要条件,并给出了原始、对偶问题的最优解和最优值的级数表达式.避免了计算逆矩阵的巨大工作.文中结果推广了诸如Robert M.FREUND等许多前人的结论.     

年龄相关的种群扩散系统的最优分布控制

本文讨论年龄相关的种群扩散系统的最优分布控制 ,证明了最优分布控制的存在性 ,得到了分布控制为最优的充分必要条件及确定最优控制的最优性组 .