Semismooth Newton method for gradient constrained minimization problem
Abstract
In this paper we treat a gradient constrained minimization problem, particular case of which is the elastoplastic torsion problem. In order to get the numerical approximation to the solution we have developed an algorithm in an infinite dimensional space framework using the concept of the generalized (Newton) differentiation. Regularization was done in order to approximate the problem with the unconstrained minimization problem and to make the pointwise maximum function Newton differentiable. Using semismooth Newton method, continuation method was developed in function space. For the numerical implementation the variational equations at Newton steps are discretized using finite elements method.
 Publication:

First International Conference on Analysis and Applied Mathematics: ICAAM 2012
 Pub Date:
 August 2012
 DOI:
 10.1063/1.4747684
 Bibcode:
 2012AIPC.1470..236A
 Keywords:

 elastoplasticity;
 finite element analysis;
 gradient methods;
 minimisation;
 Newton method;
 torsion;
 variational techniques;
 02.30.Xx;
 02.60.Pn;
 02.70.Dh;
 Calculus of variations;
 Numerical optimization;
 Finiteelement and Galerkin methods