An Interactive Method as an Aid in Solving Bicriterion Mathematical Programming Problems

In this paper, a man-machine interactive method is presented as an aid in solving the bicriterion mathematical programming problem. It is assumed that the two objective functions are real-valued functions of the decision variables which are themselves constrained to some compact and nonempty set. The overall utility function is assumed to be unknown explicitly to the decision-maker but is assumed to be a real-valued function defined on the pairs of feasible values of the objective functions and monotone non-decreasing in each argument. The decision-maker is required only to provide yes or no answers to questions regarding the desirability of increase or decrease in objective function values of solutions that he will not accept as optimal. Convergence of the method is indicated and a numerical example is presented in order to demonstrate its applicability.     

Application of Compromise Programming to a semi-detached housing development in order to balance economic and environmental criteria

European Energy Performance of Buildings Directives DE promote energy efficiency in buildings. Under these Directives, the European Union States must apply minimum requirements regarding the energy performance of buildings and ensure the certification of their energy performance. The Directives set only the basic principles and requirements, leaving a significant amount of room for the Member States to establish their specific mechanisms, numeric requirements and ways to implement them, taking into account local conditions. With respect to the Spanish case, the search for buildings that are more energy efficient results in a conflict between users’ economic objectives and society's environmental objectives. In this paper, Compromise Programming is applied to help in the decision-making process. An appropriate distribution of types of dwellings, according to their energy performance and to the climatic zone considered in Spain, will be suggested. Results provide a compromise solution between both objectives.     

运用概率方法证明某些数学不等式

在数学上一些常见的不等式的证明,若运用代数方法较难得到解决.运用概率方法较方便地证明了某些数学不等式,同时,沟通了不同学科之间的联系.     

整数规划中割平面法的研究

割平面法是求解整数规划问题常用方法之一.用割平面法求解整数规划的基本思路是:先用单纯形表格方法去求解不考虑整数约束条件的松弛问题的最优解,如果获得的最优解的值都是整数,即为所求,运算停止.如果所得最优解不完全是整数,即松弛问题最优解中存在某个基变量为非整数值时,就从最优表中提取出关于这个基变量的约束等式,再从这个约束式出发构造一个割平面方程加入最优表中,再求出新的最优解,这样不断重复的构造割平面方程,直到找到整数解为止.主要研究以下四个关键点:一是研究从最优表中提取出的、关于基变量的约束等式出发,通过将式中的系数进行整数和非负真分数的分解,从而得到一个小于等于0的另外一个不等式的推导过程;二是总结出从小于等于0的那个约束不等式出发构造割平面方程的四种方法;三是分析构造割平面方程的这四种方法相互之间的区别和联系;四是探讨割平面法的几何意义.通过对这四个方面的分析和研究,对割平面法进行透彻的剖析,使读者能够全面把握割平面法.     

问题驱动 多元表征的概念教学探究——对偶线性规划教学案例设计

数学与应用数学(师范)专业中的《运筹学》具有跨学科、实践性的课程特点,目标在于培养职前教师用数学方法解决实际问题的能力.结合义务教育阶段新课程标准中"四基"的提出这一背景,本文将以线性规划部分(运筹数学)对偶线性规划概念的引入这一知识模块为例,探讨通过问题串形式进行问题驱动、多元表征的概念教学过程.即遵循问题驱动—兴趣驱动—问题意识发展—提出和解决新问题,依据数学与外部联系、数学内部联系两条主线设计教学和学习,探索如何通过问题驱动、多元表征的结构化教学过程引导学生的学习方式发生改变,增强探究学习的动机,发展问题解决能力.课堂教学实践证明效果优于以往单一的讲授式教学法,一定程度上提高了学生的学业成绩、应用问题的兴趣和问题解决意识.     

Some Test Problems on Applications of Wu＇s Method in Nonlinear Programming Problems

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A Wildlife Management Problem: A Case Study in Multiple-Objective Linear Programming

A linear programming problem is presented to solve a problem in determining how many herbivores are needed to stock a small game reserve. The resulting problem has several conflicting objectives. The interactive algorithm which was used to solve the problem is then outlined. The interactive approach is then applied to the problem in order to find a satisfactory solution. Certain ad hoc improvisations which were needed in the final stages are outlined.     

关于几个振动定理的注记

本文通过反例指出了最近某文献中几个振动定理存在的错误.     

Hydrocarbon Field Size Distributions: A Case Study in Mixed Integer Nonlinear Programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.     

一类非凸不可微规划的算法

讨论一类带非凸不可微函数约束的非凸不可微规划的求解,提出一种基于分枝定界技巧的算法,该算法具有全局收敛性．     

Quality and Reliability: Some Recent Developments and a Historical Perspective

A general review is given of the development of ideas on quality and reliability, starting with Josiah Wedgwood in the late 18th century, through the intense activity of the 1930s, to the present, including a brief account and assessment of ideas associated with the names of Deming and Taguchi. While there is some mention of statistical aspects, no technical details are given. The second part of the paper contains comments on a number of general issues, ranging from the implications for methodological research to the potential special role of operational research and to the implications for education.     

Some Notes on a Method for Proving Inequalities by Computer

In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.     

Browder－Hartman－Stampacchia变分不等式研究概况及问题

本文介绍了Ｂｒｏｗｄｅｒ－Ｈａｒｔｍａｎ－Ｓｔａｍｐａｃｃｈｉａ变分不等式理论及应用当前研究的概况及存在的某些问题。     

Convex- and Monotone-Transformable Mathematical Programming Problems and a Proximal-Like Point Method

The problem of finding the singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will also be shown how tools of convex analysis on Riemannian manifolds can solve non-convex constrained problems in Euclidean spaces. To illustrate this remarkable fact examples will be given.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Duality in Fuzzy Linear Programming: Some New Concepts and Results

A class of fuzzy linear programming (FLP) problems based on fuzzy relations is introduced, the concepts of feasible and -efficient solutions are defined. The class of crisp (classical) LP problems and interval LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems a new concept of duality is introduced and the weak and strong duality theorems are derived. The previous results are applied to the special case of interval LP and compared to the existing literature.     

The Study for Some Subclasses of Biholomorphic Mappings by an Unified Method

LetΩ∈Cn be a bounded starlike circular domain with 0∈Ω. In this paper, we introduce a class of holomorphic mappings Mg onΩ. Let f(z) be a normalized locally biholomorphic mapping onΩsuch that Jf-1(z)f(z)∈Mg and z=0 is the zero of order k + 1 of f(z)-z. We obtain the growth and covering theorems for f(z). Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.