This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, and robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method and interior point methods.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Module 01 | |||
| Formulations | 00:20:00 | ||
| Geometry I | 00:15:00 | ||
| Geometry II | 00:15:00 | ||
| Geometry III | 00:10:00 | ||
| Simplex method I | 00:10:00 | ||
| Simplex method II | 00:15:00 | ||
| Simplex method III | 00:12:00 | ||
| Simplex method IV | 00:10:00 | ||
| Duality theory I | 00:12:00 | ||
| Duality theory II | 00:12:00 | ||
| Duality theory III | 00:10:00 | ||
| Sensitivity analysis | 00:15:00 | ||
| Module 02 | |||
| Robust optimization | 00:15:00 | ||
| Large scale optimization I | 00:15:00 | ||
| Large scale optimization II | 00:12:00 | ||
| Network flows I | 00:15:00 | ||
| Network flows II | 00:15:00 | ||
| The Ellipsoid method | 00:15:00 | ||
| Problems with exponentially many constraints | 00:10:00 | ||
| Interior point methods I | 00:12:00 | ||
| Interior point methods II | 00:15:00 | ||
| Interior point methods III | 00:10:00 | ||
| Semidefinite optimization | 00:15:00 | ||
| Discrete optimization I | 00:15:00 | ||
| Discrete optimization II | 00:12:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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