Optimization on Manifolds: Context and Applications

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Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

RTR practical aspects + tCG

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

Comparing Tangent Vectors: Three Reasons Why

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

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.

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

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

Geometry and Symmetry in Non-Convex Optimization

Delves into benign non-convexity, principal component analysis, low-rank matrix completion, and community detection in optimization.

Riemannian metrics and gradients: Why and definition of Riemannian manifolds

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Truncated Conjugate Gradients for Trust-Region Subproblem

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

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.