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Related lectures (31)

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Momentum methods and nonlinear CG

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Optimization on Manifolds: Context and Applications

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Optimization on Manifolds

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

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.

Transporters: a proxy for parallel transport

Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.

Comparing Tangent Vectors: Three Reasons Why

Explores the importance of comparing tangent vectors at different points using algorithms and finite differences.

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Truncated Conjugate Gradients for Trust-Region Subproblem

Explores truncated conjugate gradients for solving the trust-region subproblem in optimization on manifolds efficiently.

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.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.