Lectures related to RTR practical aspects + tCG

Trust Region Methods: Why, with an Example

Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.

Truncated Conjugate Gradients for Trust-Region Subproblem

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

Optimization on Manifolds: Context and Applications MOOC: Introduction to optimization on smooth manifolds: first order methods

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

Linear convergence with Polyak-Łojasiewicz: Mechanical proof

Explores linear convergence with the Polyak-Łojasiewicz condition on a Riemannian manifold.

Momentum methods and nonlinear CG

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

Gradient Descent

Covers the concept of gradient descent in scalar cases, focusing on finding the minimum of a function by iteratively moving in the direction of the negative gradient.

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Choosing a Step Size MOOC: Introduction to optimization on smooth manifolds: first order methods

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

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.

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.

Geodesic Convexity: Basic Facts and Definitions

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Quasi-newton optimization

Covers gradient line search methods and optimization techniques with an emphasis on Wolfe conditions and positive definiteness.

Nonlinear Optimization

Covers line search, Newton's method, BFGS, and conjugate gradient in nonlinear optimization.

Newton's method: Optimization on manifolds

Explores Newton's method for optimizing functions on manifolds using second-order information and discusses its drawbacks and fixes.

Optimality Conditions: First Order MOOC: Introduction to optimization on smooth manifolds: first order methods

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.

Computing the Newton Step: Matrix-Based Approaches

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Descent methods and line search: Finiteness of the line search algorithm MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Gradient Descent MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores gradient descent methods for optimizing functions on manifolds, emphasizing small gradient guarantees and global convergence.