Saving and Loading Problems

Table of Contents

• SuperSCS YAML format
• MATLAB
• C

SuperSCS YAML format

A conic problem is described by the tuple \((A,b,c,\mathcal{K})\) where \(A\) is an \(m\times n\) sparse matrix and \(\mathcal{K}\) is a cone.

These data can be saved in a YAML file from which they can be accessed from MATLAB, C, R, Java, Python and any other programming language.

YAML files are easy to parse and are human- and machine-readable.

Let us consider the following second-order cone program:

\begin{eqnarray*} &&\mathrm{Minimize}\ \langle c, x \rangle\\ &&Ax + s = b\\ &&s\in\mathcal{K}, \end{eqnarray*}

where \(x\in\mathbb{R}^3\), \(A\in\mathbb{R}^{4\times 3}\) is the following sparse matrix

\begin{eqnarray*} A &=& \begin{bmatrix} 0.3\\ & 0.7\\ && 0.2\\ -0.5 & 0.9 \end{bmatrix} \end{eqnarray*}

and \(c\in\mathbb{R}^3\) and \(b\in\mathbb{R}^4\) are the vectors

\begin{eqnarray*} c &=& \begin{bmatrix} 1 & -2 & -3 \end{bmatrix}^{\top} \end{eqnarray*}

and

\begin{eqnarray*} b &=& \begin{bmatrix} 0.2 & 0.1 & -0.1 & 0.1 \end{bmatrix}^{\top}. \end{eqnarray*}

Let \(\mathcal{K}\) be the second-order cone in \(\mathbb{R}^4\).

The YAML representation of this problem is as follows (download):

--- # SuperSCS Problem
meta:
    id: 'http://superscs.org/problem/#example-problem-1'
    date: '09-Apr-2018 19:41:52'
    creator: 'SuperSCS'
    yamlVersion: '1.2'
    license: 'https://github.com/kul-forbes/scs/blob/master/LICENSE.txt'
problem:
    name: 'example-problem-1'
    A: 
        m: 4
        n: 3
        nnz: 5
        a: [0.3,-0.5,0.7,0.9,0.2]
        I: [0,2,4,5]
        J: [0,3,1,3,2]
    b: [0.2,0.1,-0.1,0.1]
    c :[1,-2,-3]
    K:
        eq: 0
        ep: 0
        q: 4
        f: 0
        l: 0
        s: []
        ed: 0
        p: []
...

MATLAB

In MATLAB, you may serialize your problem using problem_to_yaml.

In MATLAB the data of a conic optimization problem are stored in a structure called data with fields A, b and c and another structure called K containing the cone specifications.

To save the contents of data and K in my_problem.yml run:

problem_to_yaml('my_problem.yml', 'problem-1', data, K);

To print the YAML-serialized problem data to the standard output run:

problem_to_yaml(1, 'problem-1', data, K);

To print the YAML representation to some other output stream, e.g., a stream to a file created using fopen run:

fid = fopen('path/to/myfile.yml', 'w');
problem_to_yaml(fid, 'example-problem-1', data, K);
fclose(fid);

Retrieving data from a YAML file is as simple as

[data, K] = problem_from_yaml('example.yml');

Here is a full example of saving and loading data:

filename = 'example.yml';
data.A = sparse([0.3 0 0 ; 0 0.7 0; 0 0 0.2; -0.5 0.9 0]);  % define A
data.b = [0.2; 0.1; -0.1; 0.1];                             % define b
data.c = [1;-2;-3];                                         % define c
K.eq = 0; K.ep = 0; K.q = 4;                                % define K
problem_to_yaml(filename, 'example-problem-1', data, K);    % save data
[data_loaded, K_loaded] = problem_from_yaml(filename);      % load data

A large YAML file can be found here.

C

In C, loading a YAML file is supported by SuperSCS's YAML parser.

To load a YAML file use scs_from_YAML.

Here is an example:

ScsData * data;
ScsCone * cone;
const char * filepath = "matlab/scs-yaml/example.yml";
int status = scs_from_YAML(filepath, &data, &cone);
if (status != 0) { 
 // handle failure
}
// use `data` and `cone` ...
// at the end don't forget to call `scs_free_data_cone`
scs_free_data_cone(data, cone);

To save a problem (data and cones) in a YAML file, use scs_to_YAML.

Alongside, you need to provide some metadata for your problem.

Here is an example:

const char * filepath = "my-problem.yml";
ScsData * data;
ScsCone * cone;
ScsConicProblemMetadata * metadata;
// Construct `data` and `cone` ...

// Initialize a metadata structure
metadata = scs_init_conic_problem_metadata("con-problem-1234");

// Provide some metadata
strncpy(metadata->creator, "Pantelis Sopasakis", METADATA_TEXT_SIZE);
strncpy(metadata->license, "LGPL v3.0", METADATA_TEXT_SIZE);

// Serialize to YAML and store in a file
status = scs_to_YAML(filepath, metadata, data, cone);

See Also

Sparse Matrices