Relaxed reflection methods for feasibility and matrix completion problems

可行性和矩阵完成问题的宽松反射方法

• 批准号: DP160101537
• 负责人: A/Prof Jeffrey Hogan
• 金额: $ 39.58万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-03-21 至 2021-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160101537
• 关键词: Relaxed; reflection; methods; feasibility; matrix

The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in the linear case, but does not explain many important applications for which they are often highly successful (eg optical aberration correction, protein reconstruction, tomography, compressed sensing). The project also plans to provide heuristics to help explain why an algorithm performs well on one class of applications but fails on another.

该项目建议进一步发展非线性收敛理论，并提供具体问题的实现。许多应用问题和纯问题需要求解大量的线性或非线性方程（或不等式）。高效、可并行的方法基于迭代的投影或反射算法，这些算法聚合了单个方程的信息。该理论在线性情况下得到了很好的发展，但并不能解释许多重要的应用，它们通常非常成功（例如光学像差校正，蛋白质重建，断层扫描，压缩传感）。该项目还计划提供启发式方法来帮助解释为什么一个算法在一类应用程序上表现良好，而在另一类应用程序上却失败了。