% TEST Sparse Regression: Main file for solving sparse regression problem
%                   with inexact augmented lagrangian method.
%                      minimize        ||AA(w) - b||^2
%                      subject to:     w = z.^2
%                                      |z|_2 < tau
%                                      
% 
% 
% Author: Mehmet Fatih Sahin
% Date  : 27.12.2018


clearvars
% close all

vec = @(x)reshape( x, numel( x ), 1 );
addpath(genpath('./functions/'));
addpath(genpath('./helpers/'));
%% function settings 
sparse_reg_load_data();

Ahat = [A, -A];

%% Initializations

f_grad_u = @(u, beta_, yc) [Ahat'*(Ahat*u(1:2*d) - b); zeros(2*d,1)] + 1/(beta_)*[u(1:2*d) - u(2*d+1:4*d).^2; -2*(u(1:2*d) - u(2*d+1:4*d).^2).*u(2*d+1:4*d)] + [yc; -2*yc.*u(2*d+1:4*d)];
f_u = @(u) 1/2*norm(Ahat*u(1:2*d) - b, 'fro')^2;
proj = @(u) [u(1:2*d); u(2*d+1:4*d)*min(1, sqrt(tau)/norm(u(2*d+1:4*d)))]; 
get_feas = @(u) u(1:2*d) - u(2*d+1:4*d).^2;
gamma_rule = @(beta_, yc) 1e-2; % rule for the stepsize: later add linesearch for that

%% Define algorithmic parameters and rules

beta0 = 1e0; % initial value for the penalty parameter
sigma0 = beta0*1e2; % initial value for dual step size
clearvars update_params
update_params = @(feas_cur, feas_old, k_t, iter, beta_old, sigma_old, sigma_vec, beta_vec) update_params_nonadaptive(feas_cur, feas_old, k_t, iter, beta_old, sigma_old, sigma_vec, beta_vec, sigma0, beta0);

params.averaging = 0;
params.iters = 1e4;% Number of iterations
params.verbose = 1e3;


params.Uinit = 1*rand(4*d, 1);     % In case a random initialization is used

params.ycinit = zeros(2*d,1);
params.savehist = 1;
params.startfeasible = 0; % start from a feasible point
params.gamma = 2;
params.theta = 2;

sparse_reg_cvx()
% params.x_cvx = x_cvx;


    %% Run the algorithm
[Udl, output] = linearized_augmented_lagrangian_ls(f_u, f_grad_u, proj, update_params, ...
    gamma_rule, get_feas, params);

%% Plot results
plot_results()