This section presents a numerical calculated model based on the BFGS algorithm.
This section describes a numerical optimization method with BFGS algorithm to improve simultaneously displacements and strains, and the proposed method is based on a linear function.
In case of BFGS algorithm the necessary condition for optimality is the minimization of the error function E(w).
The approximation of the Hessian inverse matrix used by BFGS algorithm is provided in the equation below:
The k + 1 step of the limited memory BFGS method is given by:
We employ a limited memory BFGS method because the Hessian matrix [B.
The LBFGS algorithm uses the BFGS formula for approximating [H.
Kauranne, The variational Kalman filter and an efficient implementation using limited memory BFGS, Internat.
The algorithms are adapted versions of the steepest descent, conjugate gradient, trust region, and BFGS
methods generalized towards manifolds.
In particular, we focus our attention on the Kalman filter itself, using the limited memory BFGS
(LBFGS)  iterative method for the required large-scale matrix storage and inversion within KF and EKF.
One is related to the DFP update and the other to the BFGS
NOCEDAL, A numerical study of the limited memory BFGS
method and the truncated-Newton method for large scale optimization, SIAM J.