Concept
Parallelizable manifold
Related lectures (11)
Unit Tangent Bundle of Hyperbolic Spaces
Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.
Tangent vectors without embedding space: Revisiting the embedded caseMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores defining tangent vectors without an embedding space, focusing on creating tangent spaces at every point of a manifold through equivalence classes of curves.
Smooth Manifolds: DiffeomorphismsMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.
Local FramesMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers the concept of local frames, their construction, and limitations.
Small Scale Stability: Equilibrium Point
Discusses stability analysis of equilibrium points in dynamical systems.
Small Scale Stability: Equilibrium Point
Covers small scale stability at equilibrium points in dynamical systems for engineers.
Constrained optimization: the basics
Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.
General Manifolds and Topology
Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Equality and Inequality Constraints: Optimization Conditions
Covers necessary optimality conditions for optimization with constraints and discusses cones and polar sets.
Single Inequality or Equality Constraint
Covers single inequality or equality constraints and necessary optimality conditions in optimization problems.