Elemental contains a variety of routines for solving optimization problems (currently, first-order methods via ADMM) as well as a collection of common utilities, such as Singular Value soft-Thresholding (SVT).

Please note that a large percentage of the following optimizaton routines were inspired by the MATLAB scripts associated with the paper:

which describes a wide variety of optimization schemes using the Alternating Direction Method of Multipliers (ADMM).