\Ell_1$ Norm

The L1 norm, representing the sum of absolute values of a vector's elements, is a crucial tool in various fields, primarily used for promoting sparsity in solutions to optimization problems. Current research focuses on its application in diverse areas, including high-dimensional data analysis (e.g., tensor recovery using L1-regularized Kaczmarz algorithms), adversarial robustness in machine learning (e.g., crafting and defending against sparse L0/L1 attacks), and efficient algorithms for problems like group testing and fair clustering. These applications highlight the L1 norm's significance in developing robust, efficient, and interpretable methods for handling complex data and mitigating challenges in machine learning and optimization.