BFGSLBFGS

BFGSLBFGS refers to a quasi-Newton optimization algorithm, specifically a limited-memory variant of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The core idea behind BFGS is to approximate the inverse Hessian matrix, which is computationally expensive to calculate directly, using gradient information. This approximation is updated iteratively to improve its accuracy over time.

The "limited-memory" aspect of L-BFGS (and thus BFGSLBFGS) means that instead of storing the full approximate inverse Hessian matrix, it stores only a limited number of past gradient and position differences. This is particularly advantageous for large-scale problems where the full Hessian would be prohibitively large to store in memory. The algorithm uses these stored vectors to reconstruct a representation of the inverse Hessian for each step.

BFGSLBFGS is widely used in machine learning and scientific computing for solving unconstrained optimization problems. Its effectiveness stems from its ability to converge relatively quickly without requiring second derivative information, while its memory efficiency makes it suitable for problems with a high number of variables. Variations of L-BFGS exist, often differing in the specific way the limited memory is managed and utilized in the update formulas.