2018/04/19 by Daria Ghilli, Karl Kunisch, Ghilli, Daria +1
Engineering · Mathematics · #49M05 49Kxx 65Kxx 74Rxx 75Pxx 49J53 49K99 #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Numerical methods in inverse problems #Optimization and Control (math.OC) #Rock Mechanics and Modeling
paper · pdf · doi:10.48550/arxiv.1804.07634
openalex publication_date 2018/04/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A general class of nonconvex optimization problems is considered, where the\npenalty is the composition of a linear operator with a nonsmooth nonconvex\nmapping, which is concave on the positive real line. The necessary optimality\ncondition of a regularized version of the original problem is solved by means\nof a monotonically convergent scheme. Such problems arise in continuum\nmechanics, as for instance cohesive fractures, where singular behaviour is\nusually modelled by nonsmooth nonconvex energies. The proposed algorithm is\nsuccessfully tested for fracture mechanics problems. Its performance is also\ncompared to two alternative algorithms for nonsmooth nonconvex optimization\narising in optimal control and mathematical imaging.\n