On the monotone and primal-dual active set schemes for $\ell^p$-type problems, $p \in (0,1]$
Optimization and Control
2017-09-20 v1 Analysis of PDEs
Numerical Analysis
Abstract
Nonsmooth nonconvex optimization problems involving the quasi-norm, , of a linear map are considered. A monotonically convergent scheme for a regularized version of the original problem is developed and necessary optimality conditions for the original problem in the form of a complementary system amenable for computation are given. Then an algorithm for solving the above mentioned necessary optimality conditions is proposed. It is based on a combination of the monotone scheme and a primal-dual active set strategy. The performance of the two algorithms is studied by means of a series of numerical tests in different cases, including optimal control problems, fracture mechanics and microscopy image reconstruction.
Keywords
Cite
@article{arxiv.1709.06506,
title = {On the monotone and primal-dual active set schemes for $\ell^p$-type problems, $p \in (0,1]$},
author = {Daria Ghilli and Karl Kunisch},
journal= {arXiv preprint arXiv:1709.06506},
year = {2017}
}