Momentum methods and nonlinear CG

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Related lectures (31)

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Optimization on Manifolds

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

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.

Optimization on Manifolds: Context and Applications

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

Choosing a Step Size

Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.

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: GD as a Matrix-Free Way

Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Optimality conditions: second order

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.