Optimization methods for mathematical programs with equilibrium constraints in function spaces based on adaptive error control and reduced order or low rank tensor approximations
基于自适应误差控制和降阶或低秩张量近似的函数空间中具有平衡约束的数学程序的优化方法
基本信息
- 批准号:314151277
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Priority Programmes
- 财政年份:2016
- 资助国家:德国
- 起止时间:2015-12-31 至 2019-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project investigates optimization methods for mathematical programs with equilibrium constraints (MPECs) in function space that adaptively control the accuracy of the underlying discretization and of inexact subproblem solves in such a way that convergence is ensured. This enables the use of adaptive discretizations, reduced order models, and low rank tensor methods, thus making the solution of MPECs with high dimensional equilibrium constraints tractable and efficient. Two prototype classes of MPECs in function space are considered in the project: One with a family of parametric variational inequalities as constraints and the other constrained by a parabolic variational inequality. Based on a rigorous analytical foundation in function space, the project will develop and analyze inexact bundle methods combined with an implicit programming approach. In addition, inexact all-at-once methods will be considered. In both cases, the evaluation of cost function, constraints, and derivatives is carried out on discretizations which are adaptively refined during optimization and can further be approximated by reduced order models or low rank tensor methods. We will develop implementable control mechanisms for the inexactness, which are tailored to the needs of the optimization methods and can be based on a posteriori error estimators. The algorithms will be implemented and tested for the considered prototype classes of MPECs.
本项目研究了函数空间中具有平衡约束(MPECs)的数学规划的优化方法,该方法自适应地控制底层离散化和不精确子问题解决的精度,以确保收敛。这使得使用自适应离散化,降阶模型,和低秩张量方法,从而使解决方案的MPEC与高维平衡约束的易处理和有效的。在该项目中考虑了函数空间中的两类原型MPEC:一类是以一族参数变分不等式作为约束,另一类是以抛物变分不等式作为约束。基于函数空间中严格的分析基础,该项目将开发和分析结合隐式编程方法的不精确束方法。此外,将考虑不精确的一次性方法。在这两种情况下,成本函数,约束和导数的评估是在优化过程中自适应细化的离散化,可以进一步近似降阶模型或低秩张量方法。我们将开发可实施的控制机制的不准确性,这是量身定制的优化方法的需要,可以基于后验误差估计。该算法将被实施和测试所考虑的原型类的MPEC。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Professor Dr. Michael Ulbrich其他文献
Professor Dr. Michael Ulbrich的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
相似国自然基金
复杂图像处理中的自由非连续问题及其水平集方法研究
- 批准号:60872130
- 批准年份:2008
- 资助金额:28.0 万元
- 项目类别:面上项目
Computational Methods for Analyzing Toponome Data
- 批准号:60601030
- 批准年份:2006
- 资助金额:17.0 万元
- 项目类别:青年科学基金项目
相似海外基金
Mathematical Optimization of Surveillance Ages to Intercept colitis-associated Colorectal cancer (MOSAIC)
监测年龄的数学优化以拦截结肠炎相关结直肠癌 (MOSAIC)
- 批准号:
10581069 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Lesion-centric optimization of multidrug therapies for tuberculosis
以病变为中心的结核病多药治疗优化
- 批准号:
10543134 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Lesion-centric optimization of multidrug therapies for tuberculosis
以病变为中心的结核病多药治疗优化
- 批准号:
10319547 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Optimization of next generation pulmonary dry powder delivery systems
下一代肺部干粉输送系统的优化
- 批准号:
9912639 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Control of heterogeneous microbial communities using model-based multi-objective optimization
使用基于模型的多目标优化控制异质微生物群落
- 批准号:
10268262 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Control of heterogeneous microbial communities using model-based multi-objective optimization
使用基于模型的多目标优化控制异质微生物群落
- 批准号:
10267334 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Construction of mathematical optimization methods for discrete data useful in machine learning algorithms.
构建可用于机器学习算法的离散数据的数学优化方法。
- 批准号:
17K19973 - 财政年份:2017
- 资助金额:
-- - 项目类别:
Grant-in-Aid for Challenging Research (Exploratory)
Optimization and joint modeling for peptide detection by tandem mass spectrometry
串联质谱肽检测的优化和联合建模
- 批准号:
9214942 - 财政年份:2017
- 资助金额:
-- - 项目类别:
Sequential Decision Making under System-inherent Uncertainty: Mathematical Optimization Methods for Time-dynamic Applications
系统固有不确定性下的顺序决策:时间动态应用的数学优化方法
- 批准号:
354864080 - 财政年份:2017
- 资助金额:
-- - 项目类别:
Research Grants
Mathematical optimization methods for healthcare improvements
改善医疗保健的数学优化方法
- 批准号:
454837-2014 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Postdoctoral Fellowships