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1.
本文先把正则化后的第二类积分方程分解为等价的一对不含积分算子K*K、仅含积分算子K以及K*的方程组, 再用截断投影方法离散方程组, 采用多层迭代算法求解截断后的等价方程组, 并给出了后验参数的选择方法, 确保近似解达到最优.与传统全投影方法相比, 减少了积分计算的维数, 保持了最优收敛率. 最后, 算例说明了算法的有效性.  相似文献   

2.
刘利斌  方虹淋 《应用数学》2020,33(2):485-495
本文讨论一类带参数的非线性奇异摄动问题的自适应移动网格方法.首先,在任意非均匀网格下,利用向后欧拉公式对方程进行离散,并给出相应的局部截断误差.然后,基于局部截断误差和网格等分布原理,利用精确解的弧长函数,证明半离散格式下自适应移动网格算法是一阶收敛的.同时,基于近似的弧长控制函数,给出易于实现的网格生成算法,并给出全离散格式下的后验误差估计.最后,数值实验结果验证了本文所给出的理论结果.  相似文献   

3.
多阶段均值-半绝对偏差模糊投资组合优化研究   总被引:1,自引:0,他引:1  
考虑交易成本和交易量限制,提出投资组合的收益率的隶属函数为梯形的多阶段均值-半绝对偏差可能性投资组合模型,并用自创算法——离散近似迭代法求解.其基本思路为:将连续型状态变量离散化,根据网络图的构造方法将上述模型转化多阶段赋权有向图;运用极大代数求出起点至终点的最长路程,即获得模型的一个可行解;以该可行解为基础,继续迭代直到前后两个可行解非常接近.文章还证明了该方法的线性收敛.最后,文章以一个具体的算例验证了该算法的有效性.  相似文献   

4.
本文提出了四种加速的BL(bundle level)算法来分别求解凸光滑函数、强凸光滑函数的极小值问题和一类鞍点(saddle-point)问题.这些算法可以运用目标函数的近似的一阶信息来得到上述几类问题的近似解.本文重点研究了在一阶信息误差上界可自由选取和给定不变的两种情形下,所提出的算法中近似解能达到的最佳精度以及相应的迭代复杂度.  相似文献   

5.
高岳林  吴佩佩 《计算数学》2017,39(3):321-327
离散填充函数是一种用于求解多极值优化问题最优解的一种行之有效的方法.已被证明对于求解大规模离散优化问题是有效的.本文基于改进的离散填充函数定义,构造了一个新的无参数填充函数,并在理论上给出了证明,提出了一个新的填充函数算法.该填充函数无需调节参数,而且只需极小化一次目标函数.数值结果表明,该算法是高效的、可行的.  相似文献   

6.
一个圆模式是指复平面C上具有特定交角的一种圆格局.给定有界单连通区域ΩC内一个具有有限多个临界点的解析函数F,首先利用有分枝圆模式枝术构造了F的离散近似解,然后证明了这个近似解序列在Ω的紧子集上一致收敛于该解析函数F.这为带有临界点的解析函数的数值计算提供一种新的方法.  相似文献   

7.
本文研究了Hilbert W*-模上的广义框架.运用了算子理论的方法,得出了Hilbert W*-模上的广义框架的一些结果,与标准离散Hilbert C*-模框架的一些结果是相似的.  相似文献   

8.
基于最速下降法的基本思想 ,提出了相互逼近算法 ,用以解决信贷风险决策过程中 ,利润曲线和风险曲线寻求公共最优近似解的问题 .该算法表明 ,当利润曲线和风险曲线不存在公共最优近似解时 ,银行追求利润最大化的结果将导致风险上升 ,无法在可接受的风险指数范围内实现其既定的盈利目标 .但当利润曲线和风险曲线存在公共最优近似解时 ,银行根据其所掌握的私有信息以及所观测到企业理性的反应 ,作出相应的决策 .公共最优近似解的存在 ,说明了银行是在风险可接受的前提下按最优性原则给企业发放贷款 .  相似文献   

9.
研究了由可乘噪声驱动的反射的椭圆随机偏微分方程网格近似解的收敛性,其中考虑区域D:=(0,1)~d,d=1,2,3.此外,还研究确定的椭圆障碍问题离散格式的解存在唯一性,并得到解关于障碍函数的连续依赖性和收敛性.  相似文献   

10.
针对随机线性互补问题,提出等价的无约束优化再定式模型,即由D-间隙函数定义的确定性的无约束期望残差极小化问题.通过拟Monte Carlo方法,将样本进行了推广,得到了相关的离散近似问题.在适当的条件下,提出了最优解存在的充分条件,以及探究了离散近似问题的最优解及稳定点的收敛性.另外,在针对一类带有常系数矩阵的随机互补线性问题,研究了解存在的充要条件.  相似文献   

11.
Multiobjective linear programming algorithms are typically based on value maximization. However, there is a growing body of experimental evidence showing that decision maker behavior is inconsistent with value maximization. Tversky and Simonson provide an alternative model for problems with a discrete set of choices. Their model, called the componential context model, has been shown to capture observed decision maker behavior. In this paper, an interactive multiobjective linear programming algorithm is developed which follows the rationale of Tversky and Simonson. The algorithm is illustrated with an example solved using standard linear programming software. Finally, an interactive decision support system based on this algorithm is developed to field test the usefulness of the algorithm. Results show that this algorithm compares favorably with an established algorithm in the field.  相似文献   

12.
In the present paper, we concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents. Furthermore, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.  相似文献   

13.
Two algorithms to solve the nonlinear bicriterion integer mathematical programming (BIMP) problem are presented. One is a noninteractive procedure that generates the entire efficient set, and the second one is an interactive procedure that determines the best compromise solution of the decision maker (DM). A Tchebycheff norm related approach is used for generating the efficient points for the BIMP problem. An application of the interactive procedure for a quality control problem is also presented.This research was supported by the National Science Foundation Grant No. ECS-82-12076 with the University of Oklahoma.  相似文献   

14.
A key feature of dynamic problems which offer degrees of freedom to the decision maker is the necessity for a goal-oriented decision making routine which is employed every time the logic of the system requires a decision. In this paper, we look at optimization procedures which appear as subroutines in dynamic problems and show how discrete event simulation can be used to assess the quality of algorithms: after establishing a general link between online optimization and discrete event systems, we address performance measurement in dynamic settings and derive a corresponding tool kit. We then analyze several control strategies using the methodologies discussed previously in two real world examples of discrete event simulation models: a manual order picking system and a pickup and delivery service.  相似文献   

15.
This paper extended the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology for solving multi-level non-linear multi-objective decision-making (MLN-MODM) problems of maximization-type. Also, two new interactive algorithms are presented for the proposed TOPSIS approach for solving these types of mathematical programming problems. The first proposed interactive TOPSIS algorithm includes the membership functions of the decision variables for each level except the lower level of the multi-level problem. These satisfactory decisions are evaluated separately by solving the corresponding single-level MODM problems. The second proposed interactive TOPSIS algorithm lexicographically solves the MODM problems of the MLN-MOLP problem by taking into consideration the decisions of the MODM problems for the upper levels. To demonstrate the proposed algorithms, a numerical example is solved and compared the solutions of proposed algorithms with the solution of the interactive algorithm of Osman et al. (2003) [4]. Also, an example of an application is presented to clarify the applicability of the proposed TOPSIS algorithms in solving real world multi-level multi-objective decision-making problems.  相似文献   

16.
As finite state models to represent a discrete optimization problem given in the form of an r-ddp (recursive discrete decision process), three subclasses of r-msdp (recursive monotone sequential decision process) are introduced in this paper. They all have a feature that the functional equations of dynamic programming hold and there exists an algorithm (in the sense of the theory of computation) to obtain the set of optimal policies. (In this sense, we may call them solvable classes of discrete dynamic programming.) Besides the algorithms for obtaining optimal policies, two types of representations are extensively studied for each class of r-msdp's. Other related decision problems are also discussed. It turns out that some of them are solvable while the rest of them are unsolvable.  相似文献   

17.
In this paper, we consider a class of nonlinear minimum-maximum optimization problems subject to boundedness constraints on the decision vectors. Three algorithms are developed for finding the min-max point using the concept of solving an associated dynamical system. In the first and third algorithms, solutions are obtained by solving systems of differential equations. The second algorithm is a discrete version of the first algorithm. The trajectories generated by the first and second algorithms may move inside or on the boundary of the constraint set, while the third algorithm ensures that any trajectory that begins inside the constraint region remains in its interior. Sufficient conditions for global convergence of the two algorithms are also established. For illustration, four numerical examples are solved.This work was partially supported by a research grant from the Australian Research Committee.  相似文献   

18.
The discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems. Recently, real quadratic congruence function fields were used to construct a public key distribution system. The security of this public key system is based on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus. This algorithm is a generalization of similar algorithms for real quadratic number fields.

  相似文献   


19.
The paper is devoted to an extension of traditional location theory in two directions. First, the usual assumption of a single cost function will be abandoned by introducing multiple objectives. This gives rise to a multidimensional programming framework for the traditional location models. The paper provides a solution algorithm for the latter problem.Next, the assumption of a uniform space will be tackled by taking account of discrete candidate-locations. This problem can be solved by means of an adjusted multiciteria analysis.The solution algorithms for both extensions are based on an interactive strategy, so that the decision-maker may identify the most favourable location in a finite number of steps.  相似文献   

20.
We propose an exact solution approach for solving nonlinear multi-objective optimization problems with separable discrete variables and a single constraint. The approach converts the multi-objective problem into a single objective problem by using surrogate multipliers from which we find all the solutions with objective values within a given range. We call this the surrogate target problem which is solved by using an algorithm based on the modular approach. Computational experiments demonstrate the effectiveness of this approach in solving large-scale problems. A simple example is presented to illustrate an interactive decision making process.  相似文献   

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