A general class of nonconvex optimization problems is considered, where the
penalty is the composition of a linear operator with a nonsmooth nonconvex
mapping, which is concave on the positive real line. The necessary optimality
condition of a regularized version of the original problem is solved by means
of a monotonically convergent scheme. Such problems arise in continuum
mechanics, as for instance cohesive fractures, where singular behaviour is
usually modelled by nonsmooth nonconvex energies. The proposed algorithm is
successfully tested for fracture mechanics problems. Its performance is also
compared to two alternative algorithms for nonsmooth nonconvex optimization
arising in optimal control and mathematical imaging.Comment: arXiv admin note: text overlap with arXiv:1709.0650
