Elemental currently supports distributed dense and sparse Linear, Quadratic, and Second-Order Cone Programs via Mehrotra Predictor-Corrector primal-dual Interior Point Methods (though geometric and semidefinite support is also planned). In addition to building on top of these backends to provide support for basis pursuit (BP), basis pursuit denoising (BPDN) / least absolute shrinkage and selection operator (LASSO), Chebyshev points (CP), Dantzig selectors (DS), non-negative least squares (NNLS), and (soft-margin) Support Vector Machines (SVM), alternating direction and operator splitting methods for more general routines are currently being explored.

Please note that the distributed sparse implementations are currently only modestly scalable due to Elemental’s current usage of 1D sparse matrix distributions (which will soon be replaced with combinations of 2D + low-rank sparse matrix distributions).