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R7172/codes/Test_bp.m
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Test_bp.m
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% TEST Basis Pursuit: Main file for solving basis pursuit
% with inexact augmented lagrangian method.
% minimize ||u||^2
% subject to: A(u.^2) = b
%
%
%
%
% Author: Mehmet Fatih Sahin
% Date : 03.01.2019
clearvars
close all
%%
vec = @(x)reshape( x, numel( x ), 1 );
addpath(genpath('./functions/'));
addpath(genpath('./helpers/'));
%% function settings
bp_load_data();
%%
Ahat = [A, -A];
%% Initializations
f_grad_u = @(u, beta_, yc) u + 1/beta_*2*u.*(Ahat'*(Ahat*(u.^2) - b)) + 2*u.*(Ahat'*yc);
f_u = @(u) 1/2*norm(u, 'fro')^2;
proj = @(u) u;
get_feas = @(u) Ahat*(u.^2) - b;
gamma_rule = @(beta_, yc) 1e-5; % rule for the stepsize: later add linesearch for that
%% Define algorithmic parameters and rules
beta0 = 1e-2; % initial value for the penalty parameter
sigma0 = beta0*1e2; % initial value for dual step size
clearvars update_parms
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 = 2e4;% Number of iterations
params.verbose = 1e3;
params.Uinit = 1*randn(2*d, 1); % In case a random initialization is used
params.ycinit = zeros(n,1);
params.savehist = 1;
params.startfeasible = 1; % start from a feasible pointf
params.gamma = 2;
params.theta = 2;
params.x_cvx = zeros(2*d, 1);
myFunc = @(u, yc, beta_) lbfgs_bp(u, Ahat, yc, b, beta_);
%%
bp_solve_cvx()
%% Run the algorithm
[Udl, output] = linearized_augmented_lagrangian_ls(f_u, f_grad_u, proj, update_params, ...
gamma_rule, get_feas, params);
%% Solve with lbfgs
beta0 = 1e-0; % initial value for the penalty parameter
sigma0 = beta0*1e2 ; % initial value for dual step size
params.iters = 2e4;% Number of iterations
params.startfeasible = 1;
params.ycinit = zeros(n,1);
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.verbose = 1e0;
[Ulbfgs, output_lbfgs, yc] = lbfgs_augmented_lagrangian(f_u, f_grad_u, proj, update_params, ...
gamma_rule, get_feas, params, myFunc);
%% Solve with apgm
beta0 = 1e-2; % initial value for the penalty parameter
sigma0 = beta0*1e2 ; % initial value for dual step size
params.iters = 2e4;% Number of iterations
params.startfeasible = 1;
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);
[Uapgm, output_apgm, yc] = apgm_augmented_lagrangian(f_u, f_grad_u, proj, update_params, ...
gamma_rule, get_feas, params, myFunc);
%% Plot result
% plot_results()
%%
plot_results_lbfgs()
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