Mathematical Programming Algorithms and Their Applications to Engineerring Problems

数学规划算法及其在工程问题中的应用

基本信息

批准号：
63490010
负责人：
KONNO Hiroshi
金额：
$ 5.5万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1990
项目状态：
已结题

项目摘要

(1) Interior point algorithms for linoar programs and linear complementarity problems.Interior point algorithms first proposed in 1984 by N. Karmarkar turned out to be the most efficient algorithms for solving large scale linear programs and linear complementarity problems. We tried to improve and polish this algorithm and obtained several new results. Some of the more important ones are ; development of the algorithm whose number of iteration is a cubic function of the number of variables ; development of primal-dual interior point algorithm ; construction of the unified theoretical framework of the interior point algorithms and the extension of the interior point algorithms to nonlinear complementarity problems.(2) Global minimization of a class of nonconvex functions over a polytope.The starting point of this research was our discovery of parametric linear programming algorithm for linear multiplicative programming problem which took place in 1989. Since then we tried to extend it t … More o diverse classes of nonconvex minimization problems such as (a) (generalized) convex multiplicative programming problems, (b) minimization of a sum (and a product) of two linear fractional functions (c) convex minimization under linear multiplicative constraints (d) minimization of a product of p convex functions (e) minimization of rank two and rank three bilinear programming problems (f) minimum cost lot-sizing problem with rho-concave cost functions. All of these problems can now be solved effectively by our algorithms.(3) Financial optimization problems.We proposed two new models in the field of portfolio optimization. One is the MAD model in which the absolute deviation is used as a measure of risk instead of the standard deviation. Second is the MADS model which enablesthe quantitative treatment of the third moment. In addition, we developed a unified framework for the multi-period portfolio-dividend optimization problems. We can now solve a large scale problem of this class which could not have been solved by existing methods. Less

（1）LinoAR程序和线性互补问题的内点算法。184在1984年提出的N. Karmarkar首次提出的算法是解决大规模线性程序和线性互补性问题的最有效算法。我们试图改进和抛光这种算法，并获得了几个新结果。一些更重要的是；算法的开发是其迭代次数是变量数量的立方函数；开发原始的偶内点算法； construction of the unified theoretical framework of the interior point algorithms and the extension of the interior point algorithms to nonlinear completerity problems.(2) Global minimization of a class of nonconvex functions over a polytope.The starting point of this research was our discovery of parametric linear programming algorithm for linear multiplicative programming problem which took place in 1989. Since then we tried to extend it … More o divers classes of非convex最小化问题，例如（a）（广义）凸面编程问题，（b）最小化两个线性分数函数的总和（和乘积）（c）在线性乘法约束（d）最小化（d）最小化p convex函数的最小值（e）等级（e）的最小化（e）级别的问题（e）中，级别的级别（e）级别（e）的最小化（e）等级（e）等级（e）的最小化（e）等级（e）级别（e）的级别（e）等级（e）等级（e）等级（E） Rho-Concave成本功能。（3）财务优化问题现在可以有效地解决所有这些问题。我们在投资组合优化领域提出了两个新模型。一种是一种疯狂的模型，其中绝对出发被用作风险的度量，而不是标准出发。第二是MADS模型，该模型可以实现第三刻的定量处理。此外，我们开发了一个统一的框架，用于多个周期投资组合 - 偏见优化问题。现在，我们可以解决此类的大规模问题，该问题无法通过现有方法解决。较少的