Optimization on Manifolds for the Numerical Solution of Equality Constrained Variational Problems

等式约束变分问题数值解的流形优化

• 批准号: 318513007
• 负责人: Professor Dr. Anton Schiela
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318513007?language=en
• 关键词: Optimization; Manifolds; Numerical; Solution; Equality

Aim of the project is to develop robust and efficient optimization methods for equality constrained problems on nonlinear manifolds. This extended framework yields additional flexibility to exploit nonlinear problem structure. We will extend an existing affine covariant composite step method to the manifold case, and exploit the benefits of its invariance properties.We will focus on two prototypical applications, which also serve as test cases to continuously evaluate and improve our algorithms. The first will be the construction of an interior point method by using the Riemannian structure of the positive cone, the second application will consider optimization problems involving Cosserat rods.

该项目的目的是发展稳健和有效的优化方法来解决非线性流形上的等式约束问题。这种扩展的框架产生了利用非线性问题结构的额外灵活性。我们将现有的仿射协变复合步长方法扩展到流形情形，并利用其不变性的优点，重点介绍了两个原型应用，这两个应用也作为测试用例，以不断评估和改进我们的算法。第一个是利用正锥的黎曼结构构造内点方法，第二个应用是考虑Cosserat杆的优化问题。

项目成果

Constrained Optimization on Manifolds

流形上的约束优化

• DOI: 10.15495/epub_ubt_00005186
• 发表时间: 2020
• 作者: J. Ortiz

Second order directional shape derivatives of integrals on submanifolds

子流形积分的二阶方向形状导数

• DOI: 10.3934/mcrf.2021017
• 发表时间: 2021
• 期刊: Mathematical Control & Related Fields
• 影响因子: 1.2
• 作者: A. Schiela;J. Ortiz
• 通讯作者: J. Ortiz

An SQP Method for Equality Constrained Optimization on Hilbert Manifolds

希尔伯特流形等式约束优化的SQP方法

• DOI: 10.1137/20m1341325
• 发表时间: 2021
• 期刊: SIAM J. Optim.
• 作者: A. Schiela;J. Ortiz
• 通讯作者: J. Ortiz