Optimization on Manifolds: Context and Applications

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Related lectures (58)

Optimization on Manifolds Log in to Mediaspace to watch this video

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Manopt: Optimization Toolbox for Manifolds Log in to Mediaspace to watch this video

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Riemannian connections Log in to Mediaspace to watch this video

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

RTR practical aspects + tCG Log in to Mediaspace to watch this video

Explores practical aspects of Riemannian trust-region optimization and introduces the truncated conjugate gradient method.

Connections: motivation and definition Log in to Mediaspace to watch this video

Explores the definition of connections for smooth vector fields on manifolds.

General Manifolds and Topology Log in to Mediaspace to watch this video

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Riemannian Gradient Descent: Convergence Theorem and Line Search Method Log in to Mediaspace to watch this video

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

All things Riemannian: metrics, (sub)manifolds and gradients Log in to Mediaspace to watch this video

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Faster Gradient Descent: Projected Optimization Techniques Log in to Mediaspace to watch this video

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Non-analytic Smooth Functions Log in to Mediaspace to watch this video

Explores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.

The Conjugate Gradients Method (CG)Log in to Mediaspace to watch this video

Covers the Conjugate Gradients method for solving linear systems iteratively with quadratic convergence and emphasizes the importance of linear independence among conjugate directions.

Differential Forms and Invariant Measures Log in to Mediaspace to watch this video

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Manifolds: Charts and Compatibility Log in to Mediaspace to watch this video

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Proximal Gradient Descent: Optimization Techniques in Machine Learning Log in to Mediaspace to watch this video

Discusses proximal gradient descent and its applications in optimizing machine learning algorithms.

Optimization in Engineering Log in to Mediaspace to watch this video

Explores optimization methods in engineering, covering decision variables, constraints, and various solving techniques.

Optimization algorithms Log in to Mediaspace to watch this video

Covers optimization algorithms, focusing on Proximal Gradient Descent and its variations.

Variance Reduction: Strategies and Applications Log in to Mediaspace to watch this video

Discusses variance reduction techniques in stochastic simulation, focusing on allocation strategies and replica generation algorithms.

Introduction to Optimization Log in to Mediaspace to watch this video

Introduces linear algebra, calculus, and optimization basics in Euclidean spaces, emphasizing the power of optimization as a modeling tool.

Optimization Techniques: Gradient Descent and Convex Functions Log in to Mediaspace to watch this video

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Riemannian Trust Regions framework Log in to Mediaspace to watch this video

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

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