Truncated Conjugate Gradients for Trust-Region Subproblem

This lecture covers the concept of truncated conjugate gradients for solving the trust-region subproblem in optimization on manifolds. The instructor introduces the trust-region subproblem and explains the strategy of running conjugate gradients cautiously and opportunistically. The lecture details the iterative process of truncated CG, emphasizing the importance of monitoring signs and boundaries to efficiently find approximate solutions. Various modifications to the CG algorithm are discussed, including early stopping criteria and checking for convergence, ensuring an effective optimization process.