Single-Variable Optimization and Line Search Fundamentals

Optimizing functions of a single variable is a fundamental building block in numerical analysis, engineering, and data science. Understanding line search algorithms and unimodal function properties allows you to solve complex mathematical problems with efficiency and accuracy. This course provides a structured introduction to the theory and application of single-variable minimization. You will build a firm grasp of essential terminology before working through iterative search methods and practical exercises. What you'll learn: • Understand foundational concepts of unimodal functions, objective functions, and local versus global minima • Master numerical search algorithms including bisection and golden section search methods • Apply derivative-based minimization techniques such as Newton-Raphson and secant methods • Analyze convergence rates, error tolerances, and stopping criteria for optimal algorithm selection • Practice solving theoretical and practical optimization problems through structured written exercises. The course moves logically from fundamental definitions to algorithmic theory and practical problem-solving. It is designed for beginners in mathematics, data science, and engineering with no prior advanced optimization background required. Begin reading today to master the foundations of single-variable optimization.