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This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim of this course is to develop the core analytical and algorithmic issues of continuous optimization. At the end of this course it teaches duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.
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 | |||
| The role of convexity in optimization | 00:25:00 | ||
| Convex sets and functions | 00:15:00 | ||
| Differentiable convex functions | 00:15:00 | ||
| Relative interior and closure | 00:15:00 | ||
| Recession cones and lineality space | 00:20:00 | ||
| Nonemptiness of closed set intersections | 00:30:00 | ||
| Review of hyperplane separation | 00:20:00 | ||
| Review of conjugate convex functions | 00:20:00 | ||
| Minimax problems and zero-sum games | 00:25:00 | ||
| Min common or max crossing Theorem III | 00:25:00 | ||
| Review of convex programming duality or counterexamples | 00:20:00 | ||
| Subgradients | 00:20:00 | ||
| Module 02 | |||
| Problem structure | 00:20:00 | ||
| Conic programming | 00:20:00 | ||
| Subgradient methods | 00:15:00 | ||
| Approximate subgradient methods | 00:20:00 | ||
| Review of cutting plane method | 00:15:00 | ||
| Generalized polyhedral approximation methods | 00:40:00 | ||
| Proximal minimization algorithm | 00:10:00 | ||
| Proximal methods | 00:20:00 | ||
| Generalized forms of the proximal point algorithm | 00:15:00 | ||
| Incremental methods | 00:15:00 | ||
| Review of subgradient methods | 00:15:00 | ||
| Gradient proximal minimization method | 00:15:00 | ||
| Convex analysis and duality | 00:30:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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