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Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Optimization on manifolds is the result of smooth geometry and optimization merging into one elegant modern framework.
We start the course at "What is a manifold?", and give the students a firm understanding of submanifolds embedded in real space. This covers numerous applications in engineering and the sciences.
All definitions and theorems are motivated to build time-tested optimization algorithms. The math is precise, to promote understanding and enable computation.
We build our way up to Riemannian gradient descent: the all-important first-order optimization algorithm on manifolds. This includes analysis and implementation.
The lectures follow (and complement) the textbook "An introduction to optimization on smooth manifolds" written by the instructor, also available on his webpage.
From there, students can explore more with numerical tools (such as the toolbox Manopt, which is the subject of the last week of the course). They will also be in a good position to tackle more advanced theoretical tools necessary for second-order optimization algorithms (e.g., Riemannian Hessians). Those are covered in further video lectures available on the instructor's textbook webpage.
By the end of the course, you will be able to:
1. Introduction
2. Manifolds and tangent spaces
3. Functions, differentials, retractions and vector fields
4. Riemannian manifolds and gradients
5. Riemannian gradient descent
6. Manopt (toolbox for optimization on manifolds)
Who can take this course?
Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.
Who can take this course?
Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.
