Geodesically Convex Optimization

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

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Convex Sets: Mathematical Optimization

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.

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.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Convex Functions: Theory and Applications

Explores convex functions, affine transformations, pointwise maximum, minimization, Schur's Lemma, and relative entropy in mathematical optimization.

Riemannian Gradient Descent: Convergence Theorem and Line Search Method

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

Conjugate Duality: Understanding Convex Optimization

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.

Optimization Techniques: Gradient Descent and Convex Functions

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.