Trust region methods: Global convergence with minimal effort

This lecture covers trust-region methods, focusing on global convergence with minimal effort. Topics include the trust-region subproblem, Cauchy step, second-order retraction, algorithm convergence, and the importance of trust region radius. The instructor explains the subproblem solver, successful steps, and parameters for optimization on manifolds. The lecture also discusses the Riemannian trust-regions (RTR) method, default parameters, and subproblem solver in Manopt, along with relaxed assumptions and finer guarantees for optimization algorithms.