Department of Applied Mathematics & Physics, Kyoto University

### Technical Report 2010-011 (August 04, 2010) SOR- and Jacobi-type Iterative Methods for Solving $\ell_1$-$\ell_2$ Problems by Way of Fenchel Duality by Masao Fukushima

We present an SOR-type algorithm and a Jacobi-type algorithm that can effectively be applied to the $\ell_1$-$\ell_2$ problem by exploiting its special structure. The algorithms are globally convergent and can be implemented in a particularly simple manner. Relations with coordinate minimization methods are discussed.