Foundations of Optimization Methods for Decision Making

In a world of limited resources and complex choices, finding the absolute best solution is a critical skill for engineers, data scientists, and business analysts. This text-based course demystifies the mathematical frameworks used to model and solve these challenging decision-making problems. You will transition from understanding basic mathematical definitions to confidently formulating and solving real-world optimization problems. By analyzing core algorithms and studying clean code implementations, you will develop a structured approach to efficiency, resource allocation, and algorithmic decision-making. What you will learn: Understand the foundational terminology and mathematical structures of linear and nonlinear programming; Apply the simplex method and network flow algorithms to solve resource allocation problems; Formulate discrete optimization challenges using branch-and-bound and cutting-plane techniques; Analyze optimality conditions for nonlinear problems using gradient-based methods and Newton's method; Explore dynamic programming concepts and optimal control principles for multi-stage decisions; Implement modern optimization formulations using standard programming libraries to solve practical scenarios. The course begins with essential definitions of variables, constraints, and objective functions before guiding you step-by-step through linear, discrete, and nonlinear algorithms. You will progress through written explanations, mathematical proofs, and clear code examples designed to solidify your conceptual understanding. This course is designed for beginners, aspiring data scientists, and analytical professionals. No prior advanced optimization background is required, though a basic comfort with algebra and introductory programming concepts will help you get the most out of the material. Start building your analytical toolkit and master the science of optimal decision-making today.