Variational Methods for Non-Linear Least-Squares

A novel feedback control system – Controlling the material flow in deep drawing using distributed blank-holder force

“…However, the proposed control problem will not converge if the Gauss-Newton scheme is applied. This observation indicates that we are dealing with a highly non-linear problem because the Gauss-Newton method is known to perform poorly in some cases, when the residuals are nonzero at the solution, or when the objective function is highly non-linear (Al-Baali and Fletcher, 1985). To overcome the converge problems the second order term was approximated; m i=1 r i (x)G i A k by the Totally Structured Secant Method (TSSM) proposed by Huschens (Huschens, 1994); additionally the Huschens scaling scheme can be combined with the projected scaling scheme (Eriksson, 1996(Eriksson, , 1999.…”

Identification of friction coefficients and hardening parameters using optimization methods coupled with a 3D finite element code

“…If the residuals or second derivatives are small, then the second-order part of the Hessian matrix approaches zero and can be neglected; this approach is known as the Gauss-Newton method. However, the method may perform poorly when the residuals are nonzero in the solution, or when the object function is highly nonlinear, see Al-Baali and Fletcher (1985). The second-order term was therefore approximated as m i=1 r i (x)G i A k by the Totally Structured Secant Method proposed by Huschens (1994).…”

Analytic Differentiation of Barlat’s 2D Criteria for Inverse Modeling

“…If the residuals or second derivatives are small, then the second order part of the Hessian matrix approaches, zero and can be neglected, this approach is known as the Gauss-Newton method. However, the method may perform poorly when the residuals are nonzero in the solution, or when the object function is highly nonlinear, [8]. Within the current setup, i.e.…”