Quasi Newton Method

Quasi-Newton methods are iterative optimization algorithms that approximate the inverse Hessian matrix to accelerate convergence towards optimal solutions, avoiding the computational cost of directly calculating the Hessian. Current research focuses on extending these methods to handle non-convex functions, nonsmooth regularized problems, and distributed or online learning settings, often employing techniques like limited-memory BFGS (L-BFGS), Anderson mixing, and novel online learning approaches for Hessian approximation updates. These advancements enhance the efficiency and applicability of quasi-Newton methods in diverse fields, including machine learning, image processing, and robotic control, particularly for large-scale problems where traditional second-order methods are computationally prohibitive.