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在一定的约束条件下极小化或极大化向量值函数,这就是向量优化. 向量优化是数学规划学科中的重要分支学科,是具有重要应用价值的、新兴的和多学科交叉的研究领域. 自1950年以来,已经逐步形成较完整的理论体系,算法研究也有一定的进展,应用日渐广泛. 简述了它的发展历程、主要特征、基本理论和方法,综述了国内学者近几年来在若干领域的发展状况和主要代表性成果,展望了向量优化学科未来的发展方向. 相似文献
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1引言变分问题是运筹学与计算数学的一个交叉研究领域.它与数学领域的其它分支如非线性规划、极大极小、不动点理论等有紧密联系,在力学、工程、经济、交通等许多实际部门有广泛的应用。但目前国内外的变分问题的理论与算法的大部分结论都是在凸锥的条件下得到的,这些结论不能直接用于非凸集上的变分问题,因为这些结论大部分都是建立在投影算子在凸集上的性质上的. 相似文献
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“线性规划”是运筹学的一个重要分支 ,它研究实际问题的某个指标最优化问题 .尽管本节“简单线性规划”只是其中最简单的部分 ,但它充分体现了数学的工具性和应用性 ,渗透着数形结合、化归等数学思想方法 ,是数学建模典型范例之一 .因此 ,教学中要充分强调建模过程 ,锻炼建模能力 .1.“线性规划”的教育价值(1)“线性规划”是培养学生“运用数学意识”和“优化思想”的良好题材 ;(2 )“线性规划”为培养学生正确的学习态度和数学学习兴趣创造了条件 ;(3)“线性规划”教学有助于发展学生分析问题的能力和运用数学知识解决实际问题的能力 .2 … 相似文献
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运筹学是应用数学的一个重要分支,在许多学科领域及工程问题中均有应用.自从运筹学在上世纪建立以来,其算法及理论的发展都受到了电子计算机的发展的极大影响.因此在本科运筹学教学中引入适当的计算机实践是非常必要的.这将有助于学生更加深入清晰地理解算法的工作步骤、算法建立的思想以及每个算法的优缺点.在本文中我们试着探讨了为何应在数学专业的运筹学教学中引入计算机实践环节,以及应当如何引入这些实践活动. 相似文献
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中国科学院数学与系统科学研究院系统科学研究所的主要创建人之一——中国工程院院士许国志研究员于2001年12月17日因病去世,他生前非常关心期刊《系统科学与数学》的发展.为了怀念先生,他过去的一些同事和不少受到他指导过的学生给《系统科学与数学》寄来了一批有关运筹学的最新研究成果.本辑收集了其中的14篇论文. 先生是中国运筹学、系统工程和系统科学的主要创建人之一.他长期致力于运筹学、系统科学、系统工程的科研、教学以及学术领导工作,发表了一系列纲领性的文献,与钱学森先生等老一辈科学家一起创建了我国运筹学、系统科学、系统工程领域的第一批研究机构、教育机构、学会和学术刊物.他指导了几代科研人员的成长,培养了一大批专门人才;积极参加、倡导、支持和推动了运筹学和系统工程在中国经济和国防建设中的应用研究;为这两个学科在中国的发展做出了重要的贡献. 相似文献
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运筹学是数学的一个分支,但又表现出除了用思维理性去思考认识客观事物的自然属性外,思维理性本身也在其研究思考之列这一明显的技术特征.它的问世开创了数学是技术的先河.从文化视野的角度观之,正是文化氛围中的数学精神才有了运筹学诞生的必然,也正是军界始终具备了与时代同步的数学素养,才有了数学被军界邀请的看似偶然实则必然的运筹学创立的契机.它昭示着,在数学是技术的今日,倡导和建立全社会的科学理性意识将是推动数学发展和改革不可缺少的外部动力与条件. 相似文献
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A family of complementarity problems is defined as extensions of the well-known linear complementarity problem (LCP). These are:
A number of well-known mathematical programming problems [namely, quadratic programming (convex, nonconvex, pseudoconvex, nonconvex), linear variational inequalities, bilinear programming, game theory, zero-one integer programming, fixed-charge problem, absolute value programming, variable separable programming] are reformulated as members of this family of four complementarity problems. A brief discussion of the main algorithms for these four problems is presented, together with some computational experience. 相似文献
(i) | second linear complementarity problem (SLCP), which is an LCP extended by introducing further equality restrictions and unrestricted variables; |
(ii) | minimum linear complementarity problem (MLCP), which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized; |
(iii) | second minimum linear complementarity problem (SMLCP), which is an MLCP, but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. |
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M. J. Best 《Journal of Optimization Theory and Applications》1982,37(3):343-353
Two important problems in the area of engineering plasticity are limit load analysis and elastoplastic analysis. It is well known that these two problems can be formulated as linear and quadratic programming problems, respectively (Refs. 1–2). In applications, the number of variables in each of these mathematical programming problems tends to be large. Consequently, it is important to have efficient numerical methods for their solution. The purpose of this paper is to present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratic programming problem which has significantly fewer variables than the original formulation. Indeed, in Section 4, we will present details of an example for which the original quadratic programming formulation required 297 variables and for which the equivalent formulation presented here required only two variables. The method is based on a characterization of the entire family of optimal solutions for a linear programming problem.This research was supported by the Natural Science and Engineering Council of Canada under Grant No. A8189 and by a Leave Fellowship from the Social Sciences and Humanities Research Council of Canada. The author takes pleasure in acknowledging many stimulating discussions with Professor D. E. Grierson. 相似文献
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G.J. Zalmai Qing-hong Zhang 《应用数学学报(英文版)》2007,23(3):353-376
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem. 相似文献
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Quantitative policy analysis problems with hierarchical decision-making can be modeled as bilevel mathematical programming problems. In general, the solution of these models is very difficult; however, special cases exist in which an optimal solution can be obtained by ordinary mathematical programming techniques. In this paper, a two-stage approach for the formulation, construction, solution, and usage of bilevel policy problem is presented. An outline of an example for analyzing Israel's public expenditure policy is also given. 相似文献
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Jørgen Tind 《Journal of Global Optimization》1991,1(2):131-144
The purpose of this article is to propose a simple framework for the various decomposition schemes in mathematical programming.Special instances are discussed. Particular attention is devoted to the general mathematical programming problem with two sets of variables. An economic interpretation in the context of hierarchical planning is done for the suggested decomposition procedure.The framework is based on general duality theory in mathematical programming and thus focussing on approaches leading to global optimality. 相似文献
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分组排序问题属于NP-难题, 单纯的数学规划模型或约束规划模型都无法在有效时间内解决相当规模的此类问题. 控制成本、缩短工期和减少任务延迟是排序问题的三个基本目标, 在实际工作中决策者通常需要兼顾三者, 并在 三者之间进行权衡. 多目标分组排序问题 的研究增强了排序问题的实际应用价值, 有利于帮助决策者处理复杂的多目标环境. 然而, 多目标的引入也增加了问题求解难度, 针对数学规划擅长寻找最优, 约束规划擅长排序的特点, 将两类方法整合起来, 提出一个基于Benders分解算法, 极大提高了此类问题的求解 效率. 相似文献
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A generalization of the mathematical model and operations research problems formulated on its basis, which were presented in [1] in the framework of an approach to planning an advertising campaign of goods and services, is considered, and corresponding nonlinear programming problems with linear constraints are formulated. 相似文献
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Wilhelm Hummeltenberg 《European Journal of Operational Research》1984,17(1):1-15
Special ordered sets (SOS) have been introduced as a practical device for efficiently handling special classes of nonconvex optimization problems. They are now implemented in most commercial codes for mathematical programming (MP software). The paper gives a survey of possible applications as multiple choice restrictions, conditional multiple choice restrictions, discrete variables, discontinuous variables and piecewise linear functions, global optimization of separable programming problems, alternative right-hand sides, overlapping special ordered sets and the solution of quadratic programming problems. Alternative problem formulations are discussed. Since special ordered sets are not defined uniquely modelling facilities depend on the definition of a special orderedset in a code. The paper demonstrates the superiority of SOS to the application of binary variables if they are treated judiciously. 相似文献