Quasi-Newton Methods
Quasi-Newton methods are iterative optimization algorithms used to find local minima or maxima of differentiable functions, particularly in unconstrained optimization problems. They approximate the Hessian matrix (second derivatives) using gradient information from previous iterations, avoiding the computational expense of calculating exact second derivatives. These methods are widely applied in machine learning, engineering design, and scientific computing for efficient large-scale optimization.
Developers should learn quasi-Newton methods when working on optimization tasks in fields like machine learning (e.g., training neural networks), data fitting, or numerical analysis, where functions are high-dimensional and computing exact Hessians is impractical. They are especially useful for problems with smooth, twice-differentiable objective functions, offering faster convergence than gradient descent while being more computationally feasible than Newton's method. Common use cases include logistic regression optimization, parameter estimation in models, and nonlinear least squares problems.