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Updated: Dec 30, 2025

Fracture Apparatus Design and Protocol Optimization for Closed-stabilized Fractures in Rodents
Published on: August 14, 2018
On a Monotone Scheme for Nonconvex Nonsmooth Optimization with Applications to Fracture Mechanics
Daria Ghilli1, Karl Kunisch1,2
11Institute for Mathematics and Scientific Computing, Karl-Franzens University, Graz, Austria.
Abstract:
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.
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