Domain-Driven Solver (DDS) Version 2.1: a MATLAB-based software package for convex optimization problems in domain-driven form
- Domain-Driven Solver (DDS) is a MATLAB-based software package for convex opti-
mization. The current version of DDS accepts every combination of the following
function/set constraints: (1) symmetric cones (LP, SOCP, and SDP); (2) quadratic
constraints that are SOCP representable; (3) direct sums of an arbitrary collection of
2-dimensional convex sets defined as the epigraphs of univariate convex functions
(including as special cases geometric programming and entropy programming); (4)
generalized Koecher (power) cone; (5) epigraphs of matrix norms (including as a
special case minimization of nuclear norm over a linear subspace); (6) vector rela-
tive entropy; (7) epigraphs of quantum entropy and quantum relative entropy; and (8)
constraints involving hyperbolic polynomials. The infeasible-start primal-dual algo-
rithms used for DDS rely heavily on duality theory and properties of Legendre-Fenchel
conjugate functions, and are designed to rigorously determine the status of a given
problem. We discuss some important implementation details and techniques we used
to improve the robustness and efficiency of the software. The appendix contains many
examples.
