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Lecture
Manopt: Optimization on Manifolds
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Related lectures (41)
Computing the Newton Step: GD as a Matrix-Free Way
Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.
From embedded to general manifolds: Why?
Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.
Computing the Newton Step: From GD to CG
Covers the transition from Gradient Descent to Conjugate Gradients, highlighting the efficiency of CG over GD in optimization on manifolds.
Tangent vectors without embedding space: Revisiting the embedded case
Explores defining tangent vectors without an embedding space, focusing on creating tangent spaces at every point of a manifold through equivalence classes of curves.
Manopt: Optimization Toolbox for Manifolds
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Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.
Riemannian connections
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Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
General Manifolds and Topology
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Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Optimization on Manifolds
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Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.
Connections: motivation and definition
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Explores the definition of connections for smooth vector fields on manifolds.
Differentiability of Functions of Several Variables
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Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.
Smooth maps on manifolds and differentials
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Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.
Covariant derivatives along curves
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Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.
Linear Systems: Iterative Methods
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Explores linear systems and iterative methods like gradient descent and conjugate gradient for efficient solutions.
Tensor Products and Symmetric Power
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Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.
Functions of LR: Differentiability
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Explains differentiability in LR functions and introduces the Jacobian matrix.
Numerical Methods: Euler and Crank-Nicolson
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Covers Euler and Crank-Nicolson methods for solving differential equations.
Determinants: Symmetric Formulas and Properties
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Explores symmetric formulas and properties of determinants, including invertibility and matrix calculations.
Vector Spaces: Bases and Dimensions
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Explores vector spaces, bases, dimensions, subspaces, and transformations.
Untitled
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Analysis: Recap and Normed Space R^n
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Covers a recap of Analysis 1 and 2, emphasizing normed space R^n, subsets, and continuous functions.
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