Evaluate students' ability to compare numerical stability, convergence rates, and computational trade-offs of Newton, quasi-Newton (e.g., BFGS/L-BFGS), and gradient-based (batch/stochastic/accelerated) methods in high-dimensional nonconvex optimization. Assess analysis of local vs. global convergence (linear, superlinear, quadratic), Hessian conditioning and eigenstructure, saddle-point behavior, step-size and line-search strategies, memory and per-iteration cost, limited-memory approximations, noise robustness, and finite-precision effects; require reasoned algorithm selection and complexity estimates.