The paper by Stephen J. Wright provides a comprehensive overview of coordinate descent (CD) algorithms, which are iterative methods used to solve optimization problems by successively minimizing along coordinate directions or hyperplanes. CD algorithms have been widely used in various applications, including data analysis, machine learning, and computational statistics, due to their efficiency and adaptability to specific problem structures. The paper covers the fundamentals of CD, including variants and extensions, and discusses their convergence properties, particularly for convex objectives. It highlights the efficiency of accelerated CD algorithms for problems with special structures, such as those arising in machine learning. The paper also explores parallel implementations of CD methods and their convergence properties under different models of parallel execution. Additionally, it addresses the relationship between CD and other optimization methods, such as stochastic gradient descent (SGD) and Gauss-Seidel methods, and provides detailed analyses of various algorithms, including randomized and accelerated variants. The paper concludes with a discussion on efficient implementations and the extension of CD methods to separable regularized problems.The paper by Stephen J. Wright provides a comprehensive overview of coordinate descent (CD) algorithms, which are iterative methods used to solve optimization problems by successively minimizing along coordinate directions or hyperplanes. CD algorithms have been widely used in various applications, including data analysis, machine learning, and computational statistics, due to their efficiency and adaptability to specific problem structures. The paper covers the fundamentals of CD, including variants and extensions, and discusses their convergence properties, particularly for convex objectives. It highlights the efficiency of accelerated CD algorithms for problems with special structures, such as those arising in machine learning. The paper also explores parallel implementations of CD methods and their convergence properties under different models of parallel execution. Additionally, it addresses the relationship between CD and other optimization methods, such as stochastic gradient descent (SGD) and Gauss-Seidel methods, and provides detailed analyses of various algorithms, including randomized and accelerated variants. The paper concludes with a discussion on efficient implementations and the extension of CD methods to separable regularized problems.