DDS (Domain-Driven Solver) version 2.2

Previous version DDS 2.1

Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form. The current version of DDS accepts every combination of the following function/set constraints:

• Symmetric cones (LP, SOCP, and SDP)
• Quadratic constraints that are SOCP representable
• 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)
• Generalized power cone
• Epigraphs of matrix norms (including as a special case minimization of nuclear norm over a linear subspace)
• Vector relative entropy
• Quantum entropy and quantum relative entropy
• Hyperbolic polynomials

DDS is a practical implementation of the infeasible-start primal-dual algorithm designed and analyzed in this paper.

DDS 2.2 is released in Dec 2023, with extensive update for quantum relative entropy (QRE) programming. The current version can solve much larger instances of QRE programming. Please see this paper.

Installation

To use DDS, the user can follow these steps:

• run MATLAB in the directory DDS;
• run the m-file DDS_startup.m.
• (optional) run the prepared small examples DDS_example_1.m and DDS_example_2.m.

The prepared examples contain many set constraints accepted by DDS and running them without error indicates that DDS is ready to use. There is a directory Text_Examples in the DDS package which includes many examples on different classes of convex optimization problems.

How to use DDS

The command in MATLAB that calls DDS is

[x,y,info]=DDS(c,A,b,cons,OPTIONS);

Input Arguments:

• cons: A cell array that contains the information about the type of constraints.
• c,A,b: Input data for DDS: A is the coefficient matrix, c is the objective vector, b is the RHS vector (i.e., the shift in the definition of the convex domain D).
• OPTIONS (optional): An array which contains information about the tolerance and initial points.

Output Arguments:

• x: Primal point.
• y: Dual point which is a cell array. Each cell contains the dual solution for the constraints in the corresponding cell in A.
• info: A structure array containing performance information such as info.time, which returns the CPU time for solving the problem.

To see how to define c,A,b,cons and how to add different types of set/function constraints, please see the users' guide.

Citing

To cite DDS software package in your work, you can cite this paper.

To cite DDS 2.2 for solving quantum relative entorpy (QRE), please additionally cite this paper.