test.m

%{
    Compute the minimum of a quadratic function f(x) = x'*Q*x + q'*x in a convex compact domain
    (Minkowski sum of unitary simplices).
%}

addpath src

% Force or not non-point-simplices
force_non_point_simplices = true;
% Space dimension, number of simplices, and the fraction of active constraints respect the solution
n = 100; K = 20; actv = 0;
% Kernel dimension, spectral radius of the matrix Q (considered only if dim_ker<n), and min strictly positive eigenvalue 
% of Q
dim_ker = 0; spectral_radius = 2; lambda_min = 1;
% Density of the matrix Q
density = 1;

% Seed for the random generator
seed = 1;
% Generate randomly the matrix Q, the vector q and the starting point x_start
[Q, q, P, K_plus, K_avg, num_vertex, norm_q, date] = GenerateInstance(n, K, force_non_point_simplices, actv, dim_ker, ...
    spectral_radius, lambda_min, density, seed);

% Save the parameters
SaveParameters(n, K_plus, K_avg, num_vertex, actv, dim_ker, spectral_radius, lambda_min, density, norm_q, seed, date)

% Save the matrices
SaveMatrices(Q, q, P, date)

% Stopping criteria for the Frank Wolfe method: max relative duality gap and max number of steps for Frank Wolfe
eps_RDG = 1e-7; max_steps = 1e6;
% Max relative error to consider the solution correct
eps_RE = 1e-10;

% Define the step size selection method: "Away-step" or "Standard"
variant = "Standard";

% Plot or not the tomography for each iteration
tomography = false;
% Plot or not the error curve
error_plot = true;
% Perform the Frank-Wolfe algorithm
[x_min, f_min, elapsed_time, num_steps, method, variant, err, converging, feasible, duality_gap, history] = ...
    FrankWolfe(Q, q, P, variant, eps_RDG, eps_RE, max_steps, tomography, error_plot, date);

% Save the results
SaveTestResults(x_min, f_min, elapsed_time, num_steps, method, variant, err, converging, feasible, duality_gap, ...
    history, date)

% Compute the Hoffman constant    
% HoffmanConstant([Q;q';P;eye(length(q))])