A LEAST-SQUARES-BASED METHOD FOR A CLASS OF NONSMOOTH MINIMIZATION PROBLEMS WITH APPLICATIONS IN PLASTICITY

This paper introduces a globally convergent algorithm for solving a class of nonsmooth optimization problems, involving square roots of quadratic forms. The class includes in particular limit analysis problems in plasticity. The algorithm combines smoothing with successive approximation. The main computational effort in each iteration is solving a linear weighted least-squares problem. The convergence of the algorithm is proved and an a priori error estimate is obtained. Numerical results are presented for two limit analysis problems.