L1 norm minimization

L1 norm minimization involves finding a solution that minimizes the sum of the absolute values of its components. Imagine adjusting a set of numbers to best fit some data, but you prefer solutions with fewer large values or many small values instead of a few big ones. By minimizing the total of their absolute sizes, L1 norm encourages sparse solutions, often leading to simpler, more interpretable models. This approach is used in areas like signal processing and machine learning to select relevant features or reduce noise, emphasizing the most important components in a dataset.