Optimization Methods and Accelerated Algorithms

Mathematical optimization powers modern machine learning, data science, and algorithmic problem-solving. This text-based course guides you through foundational optimization concepts, building a strong conceptual foundation in both classical and contemporary first-order techniques. You will gain a clear grasp of objective functions, convexity, and convergence behavior without getting lost in overly dense notation. What you'll learn: - Understand fundamental terminology, objective functions, constraints, and convex sets - Analyze standard gradient descent and subgradient methods for smooth and non-smooth optimization - Explore accelerated first-order algorithms and momentum-based techniques - Examine convergence rates, step-size selection, and condition numbers - Apply optimization principles to modern machine learning and computational problems - Practice evaluating algorithm performance through structured written exercises and conceptual walkthroughs The course begins with fundamental definitions and geometric intuitions before progressing through first-order methods, acceleration strategies, and practical computational applications. Designed for students, software engineers, and aspiring data scientists with basic algebra knowledge, this course welcomes newcomers without requiring prior advanced optimization experience. Start reading today to build a rigorous understanding of the algorithms that drive modern computation.