Linear Programming for Computer Science

Optimization is at the heart of computer science, from routing network traffic to allocating cloud resources efficiently. Linear programming provides the mathematical framework to solve these resource-allocation and decision-making problems systematically. This text-based course guides you from the fundamental concepts of linear optimization to formulating and solving real-world computer science problems. You will learn how to translate complex computational challenges into mathematical models and solve them using modern tools.\n\nWhat you'll learn:\n- Understand the core mathematical concepts of linear programming, including objective functions, constraints, and feasibility.\n- Formulate computational problems as linear programs, focusing on network flows, resource allocation, and scheduling.\n- Explore the geometry of linear programming, including the simplex method and duality theory, in an intuitive format.\n- Apply modern Python libraries to programmatically define and solve optimization models.\n- Discover how linear programming relaxation is used to design approximation algorithms for NP-hard problems.\n- Analyze the computational complexity and efficiency of different optimization algorithms.\n\nStarting with fundamental definitions and geometric intuition, the course transitions into practical formulations, duality, and modern algorithmic applications in computer science. This course is designed for beginner computer science students, software developers, and aspiring data scientists. No prior background in advanced optimization is required; basic algebra and programming concepts are sufficient. Start mastering the mathematical optimization techniques that power modern computer science algorithms today.