Time-Varying Convex Optimization: Time-Structured Algorithms and Applications

TL;DR

This paper reviews advanced algorithms for dynamic, time-varying optimization problems, emphasizing their development, analysis, and applications across various engineering fields like power systems, robotics, and machine learning.

Contribution

It provides a comprehensive overview of state-of-the-art time-varying optimization algorithms, highlighting open challenges and broad application domains.

Findings

Survey of recent algorithms for time-varying optimization

Analysis of performance and challenges in real-world applications

Illustrations in power systems, robotics, and data analytics

Abstract

Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to challenging dynamic, time-varying, and even huge-size settings. This is driven by technological transformations that converted infrastructural and social platforms into complex and dynamic networked systems with even pervasive sensing and computing capabilities. The present paper reviews a broad class of state-of-the-art algorithms for time-varying optimization, with an eye to both algorithmic development and performance analysis. It offers a comprehensive overview of available tools and methods, and unveils open challenges in application domains of broad interest. The real-world examples presented include smart power systems, robotics, machine learning, and data analytics, highlighting domain-specific issues and solutions. The ultimate goal is to exempify wide engineering relevance of analytical tools and pertinent theoretical foundations.