Design and Analysis of Algorithms for Structured Optimization

结构化优化算法的设计与分析

基本信息

批准号：
2307328
负责人：
Yunier Bello Cruz
金额：
$ 16.13万
依托单位：
Northern Illinois University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2023
资助国家：
美国
起止时间：
2023-06-15 至 2026-05-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307328&HistoricalAwards=false
关键词：
Design Analysis Algorithms Structured Optimization

项目摘要

This project aims to develop advanced tools for analyzing algorithms that solve structured optimization problems, which play an important role for models in various scientific and engineering fields, including massive data analysis, machine learning, signal processing, and image reconstruction. While there are several practical and successful algorithms for optimizing these frameworks, their fundamental convergence theory is not yet fully understood. This project seeks to develop new tools that will enable a better understanding of the core features of both the models and algorithms, design more effective algorithms, and tackle more challenging applications. The outcomes of this project will contribute to a better understanding of how to achieve fast convergence in modified classical iterations, which will improve their efficiency. The project will integrate its findings into graduate-level courses and engage Ph.D. students in research related to the project's topics.This research project will focus on designing and analyzing novel efficient projection/proximal-type schemes for solving (non)convex and (non)smooth composite optimization and feasibility problems. The research will investigate how the irregular phenomena of nonsmoothness and nonconvexity affect algorithmic performance and will study the possibility of improving the convergence complexity of the algorithms by exploiting the particular structure of the problem. Splitting iterations frequently show signs of zigzagging, affecting those schemes' convergence speed. The proposed research will advance and adapt the Circumcentered-Reflection Method to enhance the performance and complexity of splitting algorithms for solving more general structured problems. In the absence of classical assumptions, the project will also investigate variations of the FISTA algorithm for solving composite problems and semismooth Newtonian iterations for solving generalized projection equations and complementarity problems.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.

该项目旨在开发用于分析解决结构化优化问题的算法的高级工具，这些算法对于模型在各种科学和工程领域中起着重要作用，包括大量数据分析，机器学习，信号处理和图像重建。尽管有几种实用且成功的算法来优化这些框架，但它们的基本融合理论尚未完全理解。该项目旨在开发新的工具，以更好地了解模型和算法的核心特征，设计更有效的算法并解决更具挑战性的应用程序。该项目的结果将有助于更好地理解如何在修改后的经典迭代中实现快速融合，这将提高其效率。该项目将将其发现纳入研究生级课程并参与博士学位。与该项目主题相关的研究的学生。该研究项目将着重于设计和分析用于解决（非）凸（非）和（非）平滑复合优化和可行性问题的新型有效投影/近端类型方案。该研究将研究非平滑度和非凸性的不规则现象如何影响算法性能，并研究通过利用问题的特定结构来提高算法的收敛复杂性的可能性。分裂迭代经常显示曲折的迹象，影响这些方案的收敛速度。拟议的研究将推进并适应周围的反思方法，以增强分裂算法的性能和复杂性，以解决更通用的结构化问题。在没有经典假设的情况下，该项目还将调查Fista算法的变化，用于解决复合问题和半齿牛顿迭代，以解决通用投影方程和互补问题。这奖反映了NSF的法规任务，并被认为是通过基金会的知识分子的评估来评估的，并且值得通过评估的支持，并审查了基础的优质范围。