A monotone scheme for sparsity optimization in lp with p Є (0,1]

Nonsmooth nonconvex optimization problems are considered in infinite dimensional sequence spaces lp with p Є (0,1]. Our starting points are necessary optimality conditions in the form of a complementary system and a monotonically convergent algorithm for a regularized version of the original problem. We propose an algorithm for solving the necessary optimality condition based on a combination of the monotone scheme and an active-set strategy. Numerical results for different test cases are provided, e.g. for optimal control problems and microscopy image reconstruction.