Broyden–Fletcher–Goldfarb–Shanno (BFGS) Algorithm

The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is a method used in optimization to find the minimum of a function, such as minimizing costs or errors in a model. It iteratively improves estimates of the function's shape by using information about its gradient (rate of change), updating an approximation of its second derivative (curvature). This helps determine the most efficient direction to adjust variables, leading to faster convergence toward the optimal solution. BFGS is widely used because it balances accuracy and computational efficiency, making it effective for solving complex optimization problems in various scientific and engineering fields.