关于线性二级价格控制问题的注记

文［２,３,４］基于文［２］中的一条命题对价格控制问题的最优性、解集的性质及算法进行了系列研究,本文用反例说明上述有关结果所依据的命题是错的,并提出待解决的问题.     

价格控制问题解集的基本性质和连通性

价格控制问题的模型为另一类线性二级规划问题，本文对其解集的基本性质作了系统的研究和讨论。并讨论了其可行集的连通性.     

求解半向量双层规划问题的精确罚函数法

研究半向量双层规划问题的求解方法. 利用Benson’s方法及线性规划问题的对偶理论,将半向量双层规划问题转化为一个单层优化问题,同时提出了转化问题的偏静态条件定义. 基于此定义,构造了半向量双层规划的精确罚问题,得到了此类双层规划问题的最优性条件,并给出相应的求解方法. 最后通过一个数值例子表明了求解方法的可行性.     

线性二级价格控制问题的单纯形算法

主要给出求解一类双层非线性规划问题--线性二级价格控制问题的一个算法。根据问题的结构和特性，我们提出类似于线性规划单纯形算法的思想来求解线性二级价格控制问题，并用一个数值例子来说明算法如何求解。     

二层线性规划问题的遗传算法求解

对下层具有多个决策者的二层线性规划问题,提出了采用遗传算法结合线性规划方法进行求解的思想,并根据二层线性规划问题的具体特点,对遗传算法在编码、约束处理、下层问题无解处理、变异算子等方面进行了改进,最后以实例验证了算法的有效性。     

灰色二层线性规划问题及其解法

针对二层线性规划问题, 结合灰色系统的特性,提出了一般灰色二层线性规划问题, 并给出了该问题的模型及相关的定理.针对漂移型灰色二层线性规划,基于单纯形法提出了一种具有全局收敛性质的算法来求解该问题.用下层的Kuhn-Tucker条件代替下层问题,将灰色二层线性规划转化为灰色单层规划问题,利用对偶理论将该单层规划转化为一系列灰色线性规划问题,从而用单纯形法求解该问题来得到灰色二层线性规划问题的解. 最后,通过算例验证了文中算法的有效性.     

关于凸二次规划的一种算法

在本文中：１）提出了求解凸二次规划的一种算法；２）给出两个算例，它们表明该算法优于Ｗｏｌｆｅ算法和Ｌｅｍｋｅ互补转轴算法；３）作为二次规划的特殊情形。一种求解线性规划的有效算法被给出，并且与单纯形法进行了比较。     

Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.     

二层线性规划的有效解

在容许集有界且二层线性规划存在最优解是相应双目标规划有效解的假设下,证明了有效最优解可在容许集的顶点达到。给出了二层线性规划的解的更为合理的有效化方法,并用算例对各种有效化方法所得的有效解进行了比较。     

区间非线性规划问题的确定化描述及其递阶求解

讨论以区间参数形式给出的不确定性非线性规划问题,提出了一种含有决策风险因子的新的区间参数不确定非线性规划的一般命题形式,并分别就不确定性参数出现在目标函数或约束条件中的不同情况,给出不同的表达形式.文章给出用遗传算法,采用递阶优化方式求解区间参数不确定非线性规划的具体算法.仿真结果表明该形式的可行性.     

AN SQP METHOD BASED ON SMOOTHING PENALTY FUNCTION FOR NONLINEAR OPTIMIZATION WITH INEQUALITY CONSTRAINT

1 IntroductionIn tabs paper, we consider the following nonlinear optbostion problem:where j: Re - R, g: Re - Re are continuously ~ntiable functinns. SoP method forproblem (1) generates a sequence of points which converges to a K--T point of problem (1)through the following iterate formulaxk 1 = x* adds (2)adhere da is the solution of the following quadratic Prograrxuning problemin which Bh is a sylnlnetric positive deflate lllatris and A* is a stepsise obtained by some lineseaxch to redu…     

HIGH-ACCURACY FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEM

1 IntroductionOptimal design or control is playing an increasingly importal role in engineering designwork. Efficient numerical methods are among the keys to successful application of optimalcontrol in practical work. With its wide range of application in scielltific and engineeringnumerical simulation, finite element approximation of optimal control problems plays a veryimportant role in numerical method of these problems. There have been eXtensive studies inthis respect, see, for example, […     

A ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

1 IntroductionConsider the following inequality constrained optiInization problem:Inin f(x)xeRn(1)s.t. g(x) 5 0where f: R1'-R, g: R"-Rm are cofltinuousIy differentiable functions.SQP method for soIving problem(1) is to gellerate a sequence {xk} converging…     

OPTIMALITY CONDITIONS FOR NONCONVEX BILEVEL PROGRAMMING PROBLEMS

Recomendation.ThisworkisrecomendedbyamemberiftheEditorialBoard,ProfWANGShouyang.1.IntroductionThebilevelprogrammingproblemcanbestatedasfollows:whereS(x),foreachx,isthesolutionsetofthefollowingparametricprogrammingproblem:whereF,f:Re ~-R,g'Re ~-R"andG:Re ~…     

一类多目标两层决策分析及其决策方法

针对一类多目标两层决策问题，从上、下两层决策者之间的偏好关系出发，探讨了问题的决策机制：半合作决策机制与纯独立决策机制，说明了可以利用增广加权Ｔｃｈｅｂｙｃｈｅｆ范数问题来有效地表示它们的非劣解集，据此设计辅助这类多目标两层决策问题的交互式决策方法     

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming,which is a special class of bilevel programming.In our algorithm,replacing the lower level problem by its dual gap equaling to zero,the bilevel linear fractional-linear programming is transformed into a traditional single level programming problem,which can be transformed into a series of linear fractional programming problem.Thus,the modified convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming.Finally,an example demonstrates the feasibility of the proposed algorithm.     

一类非线性两级混合整数规划问题的全局最优解的近似算法

讨论了一类非线性两级混合整数规划的求解问题 .基于非线性混合整数规划理论和算法 ,探讨了对上级规划问题采用模拟退火求解混合整数规划的算法 ;对下级规划问题采用内罚函数法 .实际运算证明 ,该算法是有效的.     

一种含整数型两层决策问题的求解方法

本文利用拉格朗日松驰技巧为两层决策问题构造了简单的线性定界函数，针对上层决策变量为０－１变量的两层决策问题，提出了一种分枝定界算法。文中给出的算例说明了算法的有效性。