Enroll Course: https://www.coursera.org/learn/operations-research-theory
Operations Research (OR) is a powerful discipline that leverages mathematical and engineering methods to tackle optimization challenges across various fields, from business and economics to computer science and engineering. If you’re looking to build a robust understanding of the theoretical underpinnings of OR, then “Operations Research (3): Theory” on Coursera is an exceptional choice.
This course, the third in a series, specifically hones in on deterministic optimization techniques, a cornerstone of OR. It delves into the intricate mathematical properties that govern linear programs, integer programs, and nonlinear programs, providing a solid theoretical foundation for anyone serious about optimization.
The syllabus is thoughtfully structured, beginning with a recap of the simplex method presented in a matrix format, which is crucial for grasping subsequent lectures. The course then embarks on a comprehensive exploration of duality in linear programming. You’ll learn about primal-dual pairs, weak and strong duality, complementary slackness, and how to derive a dual optimal solution from a primal one. The practical application of shadow prices for identifying critical constraints is also a key takeaway.
Building on this, the course introduces the dual simplex method, a vital tool for sensitivity analysis, particularly for evaluating models with new constraints or variables. The network flow section is particularly impressive, covering minimum cost network flow (MCNF) models and their generalization of many famous problems like assignment, transportation, and shortest path. The discussion on total unimodularity and its connection between linear and integer programming is a highlight.
For those interested in nonlinear optimization, the course covers convex analysis and introduces Lagrangian duality and the KKT conditions for solving constrained nonlinear programs, demonstrating how linear programming duality is a special case. The practical case studies, including a facility location problem and the formulation of linear regression as a nonlinear program, along with an introduction to support-vector machines from a duality perspective, truly solidify the theoretical concepts.
Overall, “Operations Research (3): Theory” is a rigorous yet rewarding course. It’s ideal for graduate students, researchers, or professionals in fields like data science, analytics, engineering, and finance who need a deep theoretical understanding of optimization. While it requires a solid mathematical background, the instructors do an excellent job of explaining complex topics clearly. If you want to truly master the ‘why’ behind optimization algorithms, this course is highly recommended.
Enroll Course: https://www.coursera.org/learn/operations-research-theory