Foundations of Mathematical Optimization

Every business, engineering, and data science challenge boils down to making the best choice under specific constraints. Understanding mathematical optimization allows you to systematically find the most efficient, cost-effective, and high-performing solutions to complex problems. Through clear, step-by-step explanations, this text-based course guides you from foundational optimization concepts to practical formulation and modern computational solving techniques. You will learn how to translate real-world constraints into mathematical models and solve them efficiently. What you'll learn: * Learn the fundamental vocabulary and core concepts of mathematical modeling and objective functions. * Formulate and solve linear programming problems using graphical methods and the simplex algorithm. * Understand non-linear optimization techniques, including gradient-based methods used in modern machine learning. * Apply integer and multi-objective optimization models to represent complex, real-world constraints. * Explore modern computational solvers and optimization libraries, such as SciPy, to automate complex calculations. * Practice interpreting sensitivity analyses to understand how changes in constraints impact your optimal solutions. The course begins with essential terminology and the basics of mathematical formulation before moving step-by-step through linear, non-linear, and modern computational optimization methods. This course is designed for beginners in engineering, data science, economics, and business analytics, with no prior optimization experience required. Start reading today to master the mathematical tools that drive optimal decision-making.