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INTERIOR-POlNT METHODS FOR OPTIMIZATION PROBLEMS IN SOCIAL SYSTEMS

社会系统优化问题的内点方法

基本信息

批准号：
08680478
负责人：
MIZUNO Shinji
金额：
$ 1.73万
依托单位：
THE INSTITUTE OF STATISTICAL MATHEMATICS
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680478/
关键词：
OPTIMIZATION SOCIAL SYSTEM INTERIOR-POINT METHOD LlNEAR PROGRAMMING 半正定値計画問題相補性問題

项目摘要

We have performed a basic research on the interior point methods for solving optimization problems in social systems. In this year, our research mainly devoted to the development of interior point methods for linear programming and semidefinite programming, and devoted to the analysis of the global convergence and the local convergence of these methods.Most of the optimization problems iii social systems could be modeled as mathematical programming problems. The linear programming problem is the most fundamental mathematical programming problem. We performed two important research on the interior-point methods for linear programming. Firstly, in order to speed up the local convergence of interior point methods, we investigated an algorithm which trace the central path in high degree. As a result of this research, we proposed a high order infeasible interior point algorithm. Secondly, we are interested in the problem to get an initial interior point to perform an algorithm, For this purpose, we investigated two self-dual systems for linear programming, which have trivial initial points.We studied not only linear programming, but also convex programming, semidefinite programming, and semi-infinite programming. There are many search directions in interior-point methods for solving semidefinite programming problems. We investigated a self-dual subfamily of such directions. We also studied interior-point methods for solving linear and quadratic semi-infinite programming problems and proposed a dual-parameterization algorithm for convex semi-infinite programming.

对求解社会系统最优化问题的内点方法进行了基础性研究。本年度主要研究线性规划和半定规划的内点方法，并分析了这些方法的全局收敛性和局部收敛性，社会系统中的大多数优化问题都可以建模为数学规划问题。线性规划问题是最基本的数学规划问题。本文对线性规划的邻点法进行了两个重要的研究。首先，为了加快内点法的局部收敛速度，研究了一种高度跟踪中心路径的算法。作为研究的结果，我们提出了一个高阶不可行内点算法。其次，我们对求解初始内点的问题感兴趣，为此，我们研究了两个具有平凡初始点的线性规划的自对偶系统，不仅研究了线性规划，而且研究了凸规划、半定规划和半无限规划。求解半定规划问题的邻域点法有多种搜索方向。我们研究了这种方向的自对偶子族。研究了求解线性和二次半无限规划问题的邻域点法，提出了求解凸半无限规划问题的一个双参数化算法。