The Institute of Statistical Mathematics

统计数学研究所

• 批准号: 12680459
• 负责人: ITO Satoshi
• 金额: $ 2.24万
• 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: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12680459/
• 关键词: semi-infinite programming; min-max programming; nonlinear programming; convex programming; nondifferentiable optimization; infinite programming; optimal filter design; global optimization; 無限ゲーム; min-max問題; 線形計画; 2次計画; 非線型計画; 最適制御

The purpose of this research project is to develop efficient numerical methods, with a software package, for generalized semi-infinite programming (SIP). Numerical methods developed in this project include (1) an algorithm based on duality theory for solving convex SIP problems, (2) an algorithm based on local reduction within a framework of sequential quadratic programming for solving nonlinear SIP problems, (3) an algorithm based on nondifferentiable optimization theory for solving nonlinear SIP problems. We have also implemented (4) an approximation algorithm based on cutting plane strategy and (5) a two-phase algorithm based on cutting plane and local reduction. Also as further research directions, we have investigated (6) a path-following algorithm. based on continuous descent methods, together with related stiff systems of ordinary differential equations, and (7) numerical methods based on semi definite programming relaxations. Some of these numerical algorithms have been implemented and applied to problems of optimal filter design, global optimization, min-max programming, infinite games and optimal control, and these are now being compiled into a software package written in the Matlab environment, which will soon become available through our web site.

本研究项目的目的是开发有效的数值方法，与软件包，广义半无限规划（SIP）。本计画所发展的数值方法包括（1）求解凸SIP问题的基于对偶理论的算法，（2）求解非线性SIP问题的基于序列二次规划框架下的局部约简算法，（3）求解非线性SIP问题的基于不可微优化理论的算法。我们还实现了（4）基于割平面策略的近似算法和（5）基于割平面和局部约简的两阶段算法。作为进一步的研究方向，我们研究了（6）路径跟踪算法。基于连续下降法，以及相关的刚性常微分方程组，和（7）基于半定规划松弛的数值方法。其中一些数值算法已经实现并应用于最优滤波器设计，全局优化，最小最大规划，无限游戏和最优控制问题，这些问题现在正在编译成一个软件包编写的Matlab环境中，这将很快成为可通过我们的网站。

项目成果

Liu, Y. 他: "Global optimization in quadratic semiinfinite programming"Computing. 15・Supplement. 119-132 (2001)

Liu, Y. 等人：“二次半无限规划中的全局优化”15・补充119-132 (2001)。

Ito, S. 他: "An approximation approach to non-strictly convex quadratic semi-infinite programmincg"Global Optimization. (未定)(掲載予定).

Ito, S. 等人：“非严格凸二次半无限规划的近似方法”全局优化（待发布）。

S.Ito etc.: "A dual parametrization method for convex semi-infinite programming"Annals of Operations Research. (to appear).

S.Ito等：“凸半无限规划的双参数化方法”运筹学年鉴。

Ito, S.他: "An approximation approach to non-strictly convex quadratic semi-infinite programming"Journal of Global Optimization. (To appear).

Ito, S. 等人：“非严格凸二次半无限规划的近似方法”《全局优化杂志》（待发表）。

Shimizu, K., Ito, S., Otsuka, K.: "Modified direct gradient descent control of nonlinear systems"Optimization Methods and Applications, Applied Optimization (Yang, X.Q. et al (eds.)) (Kluwer Academic Publishers). 52, Chapter 8. 139-149 (2001)

Shimizu, K.、Ito, S.、Otsuka, K.：“非线性系统的改进直接梯度下降控制”优化方法和应用，应用优化（Yang，X.Q. 等人（编辑））（Kluwer 学术出版社）。