Key Information
About the content
This course blends optimization theory and computation and its teachings can be applied to modern data analytics, economics, and engineering. Organized across four modules, it takes learners through basic concepts, models, and algorithms in linear optimization, convex optimization, and integer optimization.
The first module of the course is a general overview of key concepts in linear algebra, calculus, and optimization. The second module of the course is on linear optimization, covering modeling techniques with many applications, basic polyhedral theory, simplex method, and duality theory. The third module is on convex conic optimization, which is a significant generalization of linear optimization. The fourth and final module focuses on integer optimization, which augments the previously covered optimization models with the flexibility of integer decision variables.
- Modeling skills for formulating various analytics problems as linear, convex nonlinear, and integer optimization problems.
- Basic optimization theory including duality theory and convexity theory, which will provide a deeper understanding of not only how to formulate an optimization model, but also when and why.
- Fundamental algorithmic schemes for solving linear, nonlinear, and integer optimization problems.
- Computational skills for implementing and solving an optimization problem using modern optimization modeling language and solvers.
Prerequisite
- Linear algebra
- Multivariate Calculus
- Basic probability
- Familiarity with programming in Python
Syllabus
- Module 1: Introduction
- Module 2: Illustration of the Optimization Problems
- Module 3: Review of Mathematical Concepts
- Module 4: Convexity
- Module 5: Outcomes of Optimization
- Module 6: Optimality Certificates
- Module 7: Unconstrained Optimization: Derivate Based
- Module 8: Unconstrained Optimization: Derivative Free
- Module 9: Linear Optimization Modeling – Network Flow Problems
- Module 10: Linear Optimization Modeling – Electricity Markets
- Module 11: Linear Optimization Modeling – Decision-Making Under Uncertainty
- Module 12: Linear Optimization Modeling – Handling Nonlinearity
- Module 13: Geometric Aspects of Linear Optimization
- Module 14: Algebraic Aspect of Linear Optimization
Week 8
- Module 15: Simplex Method in a Nutshell
- Module 16: Further Development of Simplex Method
- Module 17: Linear Programming Duality
- Module 18: Robust Optimization
- Module 19: Nonlinear Optimization Modeling – Approximation and Fitting
- Module 20: Nonlinear Optimization Modeling – Statistical Estimation
- Module 21: Convex Conic Programming – Introduction
- Module 22: Second-Order Conic Programming – Examples
- Module 23: Second-Order Conic Programming – Advanced Modeling
- Module 24: Semi-definite Programming – Advanced Modeling
- Module 25: Discrete Optimization: Introduction
- Module 26: Discrete Optimization: Modeling with binary variables - 1
- Module 27: Discrete Optimization: Modeling with binary variables – 2
- Module 28: Discrete Optimization: Modeling exercises
- Module 29: Discrete Optimization: Linear programming relaxation
- Module 30: Discrete Optimization: Solution methods
Instructors
Shabbir Ahmed
Anderson-Interface Chair and Professor School of Industrial & Systems Engineering
The Georgia Institute of Technology
Content Designer
Platform
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with EdX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.
