Introduction to Constrained Optimization with Python

Every real-world decision involves trade-offs and limitations, whether you are allocating a budget, designing an engineering component, or training a machine learning model. Understanding how to mathematically define and solve these constrained problems is a fundamental skill in data science, engineering, and economics. This text-based course guides you from the absolute basics of optimization to solving complex problems with multiple constraints. You will transition from theoretical understanding to writing clean, modern Python code that automates the search for optimal solutions within bounded regions. What you'll learn: - Understand foundational optimization terminology, objective functions, and feasibility regions. - Formulate mathematical models using both equality and inequality constraints. - Apply Lagrange multipliers to solve equality-constrained problems step-by-step. - Master the Karush-Kuhn-Tucker (KKT) conditions for inequality constraints. - Implement numerical solvers using modern Python libraries like SciPy to automate solutions. - Analyze real-world scenarios in finance and machine learning by translating them into optimization code. This course begins with core mathematical definitions and geometric interpretations before progressing to analytical solving techniques. Finally, you will apply these concepts programmatically, learning to structure optimization scripts with modern Python best practices and type hints. Designed for beginners in mathematical optimization, data science, or engineering, this course requires no advanced prior knowledge of optimization theory. Start reading today to master the essential mathematical tools for solving constrained problems.