Introduction to Convex Optimization

Optimization is the silent engine driving modern machine learning, engineering, and data science. Understanding how to formulate and solve convex optimization problems allows you to build more efficient algorithms and make better data-driven decisions. This written course guides you from mathematical foundations to practical algorithm implementation. You will learn how to identify convex functions, set up optimization problems, and apply standard solvers to find optimal solutions. What you'll learn: 1. Understand foundational concepts of convexity, objective functions, and mathematical constraints. 2. Identify convex sets and functions to determine if a problem has a guaranteed global minimum. 3. Apply gradient descent and its modern variants used in machine learning. 4. Formulate real-world engineering and data science problems as convex optimization models. 5. Solve optimization problems programmatically using modern Python libraries like CVXPY. 6. Analyze the convergence and efficiency of different optimization algorithms. You will start with core mathematical definitions and geometric intuition before moving on to unconstrained and constrained optimization techniques. This course is designed for beginners in data science, engineering, or applied mathematics who want a solid grasp of optimization. A basic understanding of algebra and Python is helpful, but no advanced mathematical background is required. Start reading today to unlock the mathematical core of modern algorithm design.