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Optimization on Smooth Manifolds: First-Order Methods
Master the fundamentals of optimization on nonlinear spaces, from manifold basics to Riemannian gradient descent.
Course Cost
₹ 6,369
Advanced
Skill Level
6 Weeks
Self-paced lessons
Dive into the elegant world of optimization on smooth manifolds with this advanced mathematics course. Starting from the foundational question "What is a manifold?", you'll build a robust understanding of submanifolds embedded in real space and their applications in engineering and sciences. Learn to merge smooth geometry with optimization techniques, developing the skills to recognize, analyze, and solve Riemannian optimization problems. By the end of the course, you'll be able to confidently implement and analyze first-order optimization algorithms on manifolds, opening doors to advanced applications in machine learning, computer vision, and signal processing.
English
What you'll learn
Recognize and define smooth manifolds in various contexts
Perform calculus operations on manifolds with confidence
Manipulate key concepts from differential and Riemannian geometry
Develop custom geometric tools for specific manifolds of interest
Formulate and analyze Riemannian optimization problems
Implement and analyze first-order Riemannian optimization algorithms
Use the Manopt toolbox to accelerate problem-solving and prototyping
Apply optimization on manifolds techniques to real-world engineering and scientific problems
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, exams
Access on Mobile, Tablet, Desktop
Limited Access access
Shareable certificate
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There are 6 modules in this course
This course provides a comprehensive introduction to optimization on smooth manifolds, bridging the gap between differential geometry and optimization theory. Students will gain a deep understanding of manifolds, starting from basic definitions and progressing to advanced concepts in Riemannian geometry. The curriculum covers essential topics such as tangent spaces, differentials, retractions, vector fields, and Riemannian gradients. A significant focus is placed on developing the Riemannian gradient descent algorithm, including its analysis and implementation. The course emphasizes both theoretical foundations and practical applications, equipping students with the skills to recognize and formulate Riemannian optimization problems in various fields. The final part introduces students to Manopt, a toolbox for optimization on manifolds, enhancing their ability to prototype and solve real-world problems efficiently. Throughout the course, students will develop geometric intuition and computational skills necessary for advanced work in optimization, machine learning, and related fields.
Introduction
Module 1
Manifolds and tangent spaces
Module 2
Functions, differentials, retractions and vector fields
Module 3
Riemannian manifolds and gradients
Module 4
Riemannian gradient descent
Module 5
Manopt (toolbox for optimization on manifolds)
Module 6
Fee Structure
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Faculties
These are the expert instructors who will be teaching you throughout the course. With a wealth of knowledge and real-world experience, they're here to guide, inspire, and support you every step of the way. Get to know the people who will help you reach your learning goals and make the most of your journey.
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