Ta. Laursen et Bn. Maker, AN AUGMENTED LAGRANGIAN QUASI-NEWTON SOLVER FOR CONSTRAINED NONLINEARFINITE-ELEMENT APPLICATIONS, International journal for numerical methods in engineering, 38(21), 1995, pp. 3571-3590
A solution scheme is presented for constrained non-linear equations of
evolution that result, for example, from the finite element discretiz
ation of mechanical contact problems. The algorithm discussed utilizes
a quasi-Newton non-linear equation solving strategy, with constraints
enforced by an augmented Lagrangian iteration procedure. Through pres
entation of a simple model problem and its generalization, it is shown
that the iterations associated with both the quasi-Newton algorithm a
nd the augmentation procedure can be interwoven to produce a highly ef
ficient and robust solution strategy.