Theory and computational methods of robust optimization

鲁棒优化理论与计算方法

• 批准号: 16540131
• 负责人: ITO Satoshi
• 金额: $ 2.11万
• 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: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540131/
• 关键词: robust optimization; min-max problem; cutting plane method; capacity problem; optimization in measure spaces; robust linear programming; infinite programming; optimal control; 国際情報交換; 中国; 最適制御問題; オーストラリア:中国; 非線形計画; 半無限計画; 微分不可能最適化; 大域的最適化

This research project aims at developing efficient algorithms for a class of robust optimization problem based on its theoretical analysis. Such a class of problem is represented in general as a min-max problem involving uncertainty as parameters. We first studied (1) inexact implementations of some numerical algorithms based on the cutting plane strategy, and finally proposed (2) a bilateral cutting plane framework as an ultimate solution form, whose global convergence is shown for a class of optimization problem formulated in a measure space. Furthermore we tried some refinements of the numerical framework towards its more efficient implementation with better local convergence properties. The practical side of this research project includes (3) some applications to semi-infinite programming especially for digital filter design, (4) a theoretical analysis of the asymptotic behavior of the developed framework when applied to a special case whose decision variable is limited to a class of absolutely continuous measure, and (5) some applications to optimal control problems with state variable inequality constraints. We also investigated, as related topics, (6) a type of path-following algorithm based on continuous descent methods and (7) a numerical analysis of the integration of stiff systems of ordinary differential equations.

本研究项目旨在基于理论分析，为一类鲁棒优化问题开发有效的算法。此类问题通常表示为涉及不确定性作为参数的最小-最大问题。我们首先研究了（1）基于割平面策略的一些数值算法的不精确实现，最后提出了（2）双边割平面框架作为最终解决方案形式，其全局收敛性针对以测量空间。此外，我们尝试对数值框架进行一些改进，以使其实现更有效，并具有更好的局部收敛特性。该研究项目的实践部分包括（3）半无限规划的一些应用，特别是数字滤波器设计，（4）当应用于决策变量仅限于的特殊情况时，对所开发框架的渐近行为进行理论分析一类绝对连续测度，以及（5）在具有状态变量不等式约束的最优控制问题中的一些应用。作为相关主题，我们还研究了（6）一种基于连续下降方法的路径跟踪算法和（7）常微分方程刚性系统积分的数值分析。

项目成果

A numerical solution of state-constrained optimal control problems by dual sequential quadratic programming with cutting plane strategy

状态约束最优控制问题的割平面策略对偶顺序二次规划数值求解

• 发表时间: 2005
• 期刊: Proceedings of the Institute of Statistical Mathematics 53/2
• 作者: Ito;S.
• 通讯作者: S.

A path following method for solving a class of semi-infinite programming problems

求解一类半无限规划问题的路径跟踪方法

• 发表时间: 2004
• 期刊: Abstracts of OCA 2004 n/a
• 作者: Ito;S.;Shimizu;K.
• 通讯作者: K.

双対逐次2次計画および切除平面法による状態制約最適制御問題の解法

使用对偶顺序二次规划和割平面法求解状态约束最优控制问题

• 发表时间: 2005
• 期刊: 統計数理 53・2
• 作者: Ito;S.;伊藤 聡
• 通讯作者: 伊藤 聡

An approximation approach to non-strictly convex quadratic semi-infinite programming

非严格凸二次半无限规划的逼近方法

• 发表时间: 2004
• 期刊: Journal of Global Optimization 30/2-3
• 作者: Ito;S.;Liu;Y.;Teo;K.L.
• 通讯作者: K.L.

Nonlinear dynamical programming via direct gradient descent control

通过直接梯度下降控制的非线性动态规划

• 发表时间: 2004
• 期刊: Proceedings of the 6 ICOTA (cdrom) n/a
• 作者: Shimizu;K.;Ito;S.
• 通讯作者: S.