Gradient Methods

 

 

 

Properties of BFGS

The BFGS algorithm has several key properties that make it widely used:

  1. \textbf{No need for second derivatives:} The BFGS method approximates the Hessian matrix and avoids the direct computation of second derivatives.
  2. \textbf{Superlinear convergence:} The BFGS method typically converges faster than gradient descent methods, especially near the optimum.
  3. \textbf{Memory efficiency:} The BFGS algorithm maintains a low-rank approximation of the inverse Hessian, making it computationally efficient.
  4. \textbf{Positive definiteness:} If the initial Hessian approximation is positive definite, the BFGS update preserves this property.