CIF: Small: A Simple and Unifying Optimization Framework for Signal and Information Processing Problems with Min-Max Structures

在过去的二十年里，信号和信息处理的进步在很大程度上受到了最优化方面的新发展的影响。从线性规划到凸优化的现代优化方法已经成为解决压缩传感、生物信息学、无线通信和数据分析等核心应用领域中出现的问题的不可或缺的工具。同时，信号处理应用的优化算法的巨大增长要求开发统一的框架，它可以帮助我们简化对算法行为的理解，预测性能，并简化特定于应用的算法的设计。该项目开发的框架将使信号处理以外的广泛应用受益，包括机器学习、数据挖掘和计算机视觉。拟议的努力还为本科生参与跨学科研究以及K12外联活动提供了丰富和多样的机会。该项目致力于设计一个框架来处理一类具有挑战性的块最小化-最大化问题，该问题涉及联合最小化和最大化一类特定的结构化目标函数。这涵盖了许多新旧信号处理应用，例如最小速率效用最大化和强大的数据分析。这个项目将采取自下而上的方法，从相对简单的公式开始，逐步构建特定于问题的功能和属性。将进行严格的性能分析，所产生的算法将在许多信号处理应用程序中进行专门化和评估，包括在存在干扰器的情况下进行无线资源分配。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Over the past two decades, advances in signal and information processing have been heavily influenced by new developments in optimization. Modern optimization methods, from linear programming to convex optimization, have become indispensable tools to approach problems that arise in a number of core application areas such as compressive sensing, bioinformatics, wireless communication, and data analytics. Meanwhile, the tremendous growth in optimization algorithms for signal processing applications calls for the development of unifying frameworks, which can help simplify our understanding of algorithmic behavior, predict performance, and streamline the design of application-specific algorithms. The framework developed in this project will benefit a wide range of applications well beyond signal processing, including machine learning, data mining and computer vision. The proposed efforts also offer rich and varied opportunities for engaging undergraduate students in cross-disciplinary research, as well as in K12 outreach activities. This project is focused on designing a framework that deals with a challenging class of block Minimization-Maximization problems, which involves jointly minimizing and maximizing a particular class of structured objective functions. This covers many signal processing applications, old and new, such as min rate utility maximization and robust data analytics. This project will take a bottom-up approach, where starting from a relatively simple formulation, problem-specific features and properties will be gradually built. Rigorous performance analysis will be conducted, and the resulting algorithms will be specialized and evaluated in a number of signal processing applications, including wireless resource allocation in the presence of jammers.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.