Lasso Regression and Subgradient Descent in Convex Optimization

When building predictive models, selecting the most impactful features while preventing overfitting is a constant challenge. Standard gradient descent fails when dealing with the sharp corners of L1 regularization, making it essential to understand how optimization works when derivatives do not exist. This text-based course guides you through the mathematical foundations and practical implementation of subgradient descent to solve Lasso regression. You will learn how to handle non-differentiable objective functions, understand the mechanics of convex optimization, and implement sparse models from the ground up. What you will learn: Understand the core principles of convex optimization and the geometric intuition behind L1 regularization; Calculate subgradients and subdifferentials for non-differentiable functions; Implement the subgradient descent algorithm for Lasso regression using clean Python code; Analyze how Lasso performs automatic feature selection by driving coefficients to absolute zero; Evaluate model performance and tune regularization hyperparameters using modern validation workflows; Practice debugging convergence issues common in non-smooth optimization. You will begin with foundational mathematical definitions and key terminology before moving step-by-step through algorithm design and code implementation. This course is designed for beginners in mathematical optimization and machine learning who have a basic familiarity with Python and linear algebra. Start reading today to master the core optimization techniques that power modern sparse machine learning models.