The proximal augmented Lagrangian method for distributed and embedded nonsmooth composite optimization

用于分布式嵌入式非光滑复合优化的近端增广拉格朗日方法

基本信息

批准号：
1809833
负责人：
Mihailo Jovanovic
金额：
$ 36万
依托单位：
University of Southern California
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-15 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1809833&HistoricalAwards=false
关键词：
proximal augmented Lagrangian method distributed

项目摘要

Large networks of dynamical systems that combine sensing, computing, and communication devices are ubiquitous in modern technology. One of the major challenges in networked systems is the development of fast and scalable methods for their analysis and design. Such systems involve large-scale interconnections of components, have rapidly-evolving structure and limitations on communication/processing power, and require real-time distributed control actions. These requirements make control strategies that rely on centralized information processing infeasible and motivate new classes of optimal control problems. In these, standard performance metrics are augmented with typically nonsmooth regularizers to promote desired structural features (e.g., low communication requirements) in the optimal controller. The broader impacts of the proposed work range from improved performance and reliability of power grid to systematic design of combination drug therapies for HIV treatment. The educational part of the proposal focuses on the development of new nonlinear and distributed systems curricula. The PI will develop new introductory courses aimed at attracting students from diverse engineering departments at senior undergraduate and first year graduate levels. The courses will emphasize practical applications, physical interpretations, structural features, and common themes in analysis and design of nonlinear and networked systems. The intellectual merit lies in the development of theory and techniques for distributed and embedded nonsmooth composite optimization. Structured optimal control and inverse problems, that arise especially when trying to identify and control dynamical representations of rapidly evolving systems in real-time, typically lead to optimization of functionals consisting of a sum of a smooth term and a nonsmooth regularizer. The PI's recent research will be leveraged to develop theoretical foundation and methods for solving these problems efficiently and reliably. The cornerstone of this proposal is the proximal augmented Lagrangian, a continuously differentiable function of primal and dual variables that enables the development of variety of first and second order methods for nonsmooth composite optimization. The PI will utilize structure of proximal operators associated with nonsmooth regularizers to develop efficient algorithms for large-scale distributed and embedded optimization and employ control-theoretic tools to establish their convergence rates. The proposed effort will furnish new classes of first and second order primal-dual algorithms for nonsmooth composite optimization, lead to significant advances in control-oriented and physically-viable modeling, and enable real-time distributed control of large-scale networks of dynamical systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

结合感应，计算和通信设备的动力学系统的大型网络在现代技术中无处不在。网络系统中的主要挑战之一是开发其分析和设计的快速和可扩展方法。这样的系统涉及组件的大规模互连，具有快速发展的结构和通信/处理能力的局限性，并且需要实时分布式控制操作。这些要求使控制策略依靠集中式信息处理不可行，并激发新的最佳控制问题类别。在这些中，标准性能指标通常使用非平滑的正规化器增强，以促进最佳控制器中所需的结构特征（例如，沟通需求低）。拟议工作的更广泛的影响范围从提高的性能和电网的可靠性到对HIV治疗的组合药物疗法的系统设计。该提案的教育部分着重于开发新的非线性和分布式系统课程。 PI将开发新的入门课程，旨在吸引高级本科和第一年研究生水平的不同工程系的学生。这些课程将在非线性和网络系统的分析和设计中强调实用应用，物理解释，结构特征以及共同主题。智力优点在于开发分布式和嵌入式非平滑复合材料优化的理论和技术。结构化的最佳控制和反问题，尤其是在试图实时识别和控制快速发展系统的动态表示时会出现的，通常会导致优化由平稳期限和非平滑正常使用器组成的功能。 PI最近的研究将被利用，以开发理论基础和方法来有效，可靠地解决这些问题。该提案的基石是近端的增强拉格朗日，这是原始和双重变量的不断区分功能，它可以开发多种一阶和二阶方法，以进行非平面复合优化。 PI将利用与非平滑正规化器相关的近端运算符结构来开发用于大规模分布式和嵌入式优化的有效算法，并使用控制理论工具来确定其收敛速率。 The proposed effort will furnish new classes of first and second order primal-dual algorithms for nonsmooth composite optimization, lead to significant advances in control-oriented and physically-viable modeling, and enable real-time distributed control of large-scale networks of dynamical systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.