Foundations of Convex Optimization for Engineering and Machine Learning

Optimization is at the heart of modern decision-making, from training neural networks to designing efficient financial portfolios. Understanding how to formulate and solve these problems mathematically allows you to find globally optimal solutions efficiently. This text-only course guides you through the core principles of convex optimization, transforming complex mathematical theory into practical modeling skills. You will learn to recognize convex problems in the wild, formulate them mathematically, and solve them using modern computational libraries. What you will learn: Understand the fundamental definitions of convex sets, functions, and optimization problems; Formulate real-world problems as linear, quadratic, or semidefinite programs; Apply optimality conditions and duality theory to analyze and simplify complex mathematical models; Solve practical optimization tasks in machine learning, signal processing, and portfolio design; Practice writing clean, modern Python code using CVXPY to numerically solve convex formulations. The course begins with foundational mathematical concepts and definitions before progressing to structured optimization types and duality theory. You will then explore practical applications across various industries through written walkthroughs and programmatic examples. Designed for beginners in mathematical optimization, this course requires only a basic understanding of linear algebra and calculus, starting with key terminology from the ground up. Begin your journey into mathematical modeling and unlock the power of guaranteed optimal solutions today.