# Domain-Driven Solver (DDS) Version 2.0: a MATLAB-based Software Package for Convex Optimization Problems in Domain-Driven Form

## TL;DR

Domain-Driven Solver 2.0 is a MATLAB software package that efficiently solves a wide range of convex optimization problems using an infeasible-start primal-dual algorithm, with extensive examples and implementation insights.

## Contribution

This paper introduces DDS 2.0, expanding the types of convex problems it can handle and providing detailed implementation and efficiency improvements.

## Key findings

- Supports diverse convex constraints including symmetric cones and quantum entropy
- Provides practical implementation details and efficiency techniques
- Includes numerous examples demonstrating solver capabilities

## Abstract

Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [Karimi and Tun\c{c}el, arXiv:1804.06925]. 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 power cone; (5) epigraphs of matrix norms (including as a special case minimization of nuclear norm over a linear subspace); (6) vector relative entropy; (7) epigraphs of quantum entropy and quantum relative entropy; and (8) constraints involving hyperbolic polynomials. DDS is a practical implementation of the infeasible-start primal-dual algorithm designed and analyzed in [Karimi and Tun\c{c}el, arXiv:1804.06925]. This manuscript contains the users' guide, as well as theoretical results needed for the implementation of the algorithms. To help the users, we included many examples. We also discussed some implementation details and techniques we used to improve the efficiency and further expansion of the software to cover the emerging classes of convex optimization problems.