Homec4science
Diffusion Nonlinear (master) Browse

R7172/codes/Test_generalized_eigenvalue.m
a88af8580e6amaster

Last Change
Raw File

Test_generalized_eigenvalue.m
View Options

% TEST Generalized eigenvalue: Main file for solving sdp relaxation of maxcut problem using
% inexact augmented lagrangian method.
% minimize u'Cu
% subject to: u'Bu = 1
%
%
% Author: Mehmet Fatih Sahin
% Date : 23.11.2018
clearvars
% close all
vec = @(x)reshape( x, numel( x ), 1 );
addpath(genpath('./functions/'));
addpath(genpath('./helpers/'));
%% function settings
gen_eig_load_data();
normB = normest(B);
normC = normest(C);
%% Initializations
f_grad_u = @(u, beta, yc) (2*(1/beta)*(A_id(u, u) - 1)*(B*u) - 2*(C*u)) + 2*yc*(B*u);
f_u = @(u) -sum(vec(u .* (C*u)));
proj = @(u) u;
get_feas = @(u) A_id(u, u) - 1;
gamma_rule = @(beta_, yc) beta_/(2*normB^2+2*beta_*normC+2*normB*abs(beta_*yc-1));
%% Define algorithmic parameters and rules
r = 1; % target rank: you may set it sqrt(n)
beta0 = normC/1e0; % initial value for the penalty parameter
sigma0 = beta0*1e1; % initial value for dual step size
update_params = @(feas_cur, feas_old, k_t, iter, beta_old, sigma_old, sigma_vec, beta_vec) update_params(feas_cur, feas_old, k_t, iter, beta_old, sigma_old, sigma_vec, beta_vec, sigma0, beta0);
params.averaging = 0;
params.iters = 1e5;% Number of iterations
params.verbose = 1e3;
params.Uinit = randn(n, r); % In case a random initialization is used
params.ycinit = 0;
params.savehist = 1;
params.startfeasible = 1; % start from a feasible point
%% Run the algorithm
[Udl, output] = linearized_augmented_lagrangian(f_u, f_grad_u, proj, update_params, ...
gamma_rule, get_feas, params);
%% Plot results
gen_eig_solve()
%%
plot_results()
figure(f)
hold on; loglog(abs(objective - opt_val)/abs(opt_val), '--b', 'Linewidth', lw)
legend({'Linearized AL', 'GenELin'}, 'Interpreter', 'Latex', 'Location', 'best')
c4science · Help