Convex Optimization

Deterministic optimization is the cornerstone for understanding modern MCMC algorithms (like HMC, Langevin). This article delves into three classic deterministic optimization strategies: Newton’s Method (second-order perspective using curvature), Coordinate Descent (the divide-and-conquer predecessor to Gibbs), and Steepest Descent (greedy first-order exploration). Through mathematical derivation and Python visualization, we compare their behavioral patterns and convergence characteristics across different terrains (convex surfaces, narrow valleys, strong coupling). [Read More]