Nonlinear Optimization Algorithms for Large-Scale and Nonsmooth Applications

适用于大规模和非光滑应用的非线性优化算法

• 批准号: 1016291
• 负责人: Frank Curtis
• 金额: $ 11万
• 依托单位: Lehigh University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016291&HistoricalAwards=false
• 关键词: Nonlinear; Optimization; Algorithms; Large; Scale

The investigator, his colleagues, and his students study the development, analysis, and implementation of algorithms for large-scale PDE-constrained and nonsmooth optimization. The novelty of the work in both of these frameworks is that in each case the investigator and his group are finding powerful ways in which the most advanced methods for nonlinear programming can be enhanced and broadened to remain effective for application areas in which they have previously been inefficient or inapplicable. In the context of large-scale PDE-constrained problems, such as those in optimal design, parameter estimation, and image registration, this is being achieved by removing the need for the factorization of matrices and allowing for inexactness in the solution of large-scale linear systems, while still guaranteeing convergence to a solution point. In the context of nonsmooth applications, such as those in compressed sensing and robust stability and control, this is being achieved by enhancing leading algorithmic frameworks through a process of gradient sampling, allowing for a loosening of the assumption that the problem functions are differentiable everywhere. These works in these fields tie together algorithms and computational techniques from diverse areas, and both numerical methods and convergence theory are being provided.The broader impact of this project is that it advances pencil-and-paper engineering ideas to the point where they can be implemented in high-performance computing software and are able to solve challenging problems in the design and analysis of complex systems. For example, there is a high demand for optimization tools such as these in healthcare, particularly in the area of cancer treatment and therapy. By providing doctors and medical technicians with novel computational tools, they will be able to optimally administer hyperthermia treatment in a manner that takes into account the inner complexities of the human body, such as blood flow. They will also be able to effectively and adaptively design plans for radiation therapy that minimize damage to healthy -- and often critical -- tissue near the target area(s). Amazingly enough, these same computational tools can also be employed in medical image registration, aiding medical professionals in the detection of irregularities over time and between different (e.g., PET, CT, MRI) scans. The goal in all of these areas is to provide the user with sophisticated software that can answer, in real-time, difficult questions such as "What is the optimal way of administering this radiation?" and "Is there anything in this image that has changed or is cause for alarm?"

研究人员，他的同事和他的学生研究大规模PDE约束和非光滑优化算法的开发，分析和实现。 在这两个框架中的工作的新奇在于，在每种情况下，研究人员和他的团队都在寻找强有力的方法，可以增强和扩展非线性规划的最先进方法，以保持对以前效率低下或不适用的应用领域的有效性。 在大规模的偏微分方程约束的问题，如在优化设计，参数估计和图像配准的背景下，这是通过消除矩阵的因式分解的需要，并允许在大规模线性系统的解决方案的不精确性，同时仍然保证收敛到一个解决方案点。 在非光滑应用的背景下，如压缩传感和鲁棒稳定性和控制，这是通过增强领先的算法框架，通过梯度采样过程，允许放松的假设，问题的功能是可微无处不在。 这些领域的工作将不同领域的算法和计算技术结合起来，提供数值方法和收敛理论。该项目的更广泛影响是，它将纸上工程思想推进到可以在高性能计算软件中实现的程度，并能够解决复杂系统设计和分析中的挑战性问题。 例如，在医疗保健领域，特别是在癌症治疗和疗法领域，对优化工具的需求很高。 通过为医生和医疗技术人员提供新的计算工具，他们将能够以考虑到人体内部复杂性（如血流）的方式进行最佳的热疗治疗。 他们还将能够有效地和自适应地设计放射治疗计划，最大限度地减少对目标区域附近健康组织（通常是关键组织）的损害。 令人惊讶的是，这些相同的计算工具也可以用于医学图像配准，帮助医学专业人员检测随着时间的推移以及不同（例如，PET、CT、MRI）扫描。 所有这些领域的目标都是为用户提供复杂的软件，可以实时回答诸如“管理这种辐射的最佳方式是什么？以及“这幅图中有没有什么变化或引起恐慌的地方？“"