kvasikohandamismeetodid

Kvasikohandamismeetodid, also known as quasi-Newton methods, are iterative algorithms used in numerical optimization to find the minimum of a function. These methods approximate the Hessian matrix, which contains second-order partial derivatives of the objective function, rather than calculating it directly. This approximation is updated at each iteration, making the methods more efficient than traditional Newton's method, especially for functions where computing the Hessian is computationally expensive or impossible.

The core idea behind quasi-Newton methods is to use the gradient information from previous steps to build an approximation of the Hessian or its inverse. Common update formulas include the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm and the Davidon–Fletcher–Powell (DFP) algorithm. These methods typically achieve superlinear convergence, which is faster than gradient descent but generally slower than the quadratic convergence of Newton's method.

Quasi-Newton methods are widely applied in various fields, including machine learning, econometrics, and engineering, due to their balance between computational cost and convergence speed. They are particularly useful when the objective function is smooth but its second derivatives are difficult to obtain. The choice of a specific quasi-Newton method often depends on the problem's characteristics and the desired trade-off between memory usage and convergence rate.