diff --git a/codes/convex_example_bp/bp_nonconvex_adap.m b/codes/convex_example_bp/bp_nonconvex_adap.m
new file mode 100755
index 0000000..2eef019
--- /dev/null
+++ b/codes/convex_example_bp/bp_nonconvex_adap.m
@@ -0,0 +1,179 @@
+clear all
+
+scale       = 1;
+p           = scale*100;
+n           = scale*40; 
+s           = scale*1; 
+
+A           = normr(randn(n, p));
+x_org       = zeros(p, 1);
+T           = randsample(p, s);
+x_org(T)    = randn(s, 1);
+sigma       = 1e-4;
+b           = A*x_org + sigma*randn(n, 1);
+
+%% Solve by CVX
+cvx_precision best;
+cvx_solver SDPT3
+cvx_begin
+   variable x_cvx(p);
+   minimize( (norm(x_cvx, 1)) );
+   subject to
+       A*x_cvx == b;
+cvx_end
+fopt = cvx_optval;
+probParams.x_cvx        = x_cvx;
+
+%% constant params
+
+prox_l1 = @(x, tau) sign(x).*max(abs(x)-tau, 0);
+obj = @(x) norm(x,1);
+LA = norm(full(A));
+
+beta0 = 1e-1;
+beta = beta0;
+sigma0 = beta0*(1e1);
+
+x0 = zeros(p, 1);
+x = x0;
+y0 = zeros(n, 1);
+y = y0;
+maxit = 1e5;
+obj_vec_const = zeros(maxit, 1);
+feas_const = zeros(maxit, 1);
+betas = zeros(maxit, 1);
+sigmas = zeros(maxit, 1);
+sigma = sigma0;
+k0= 0;
+feas = norm(A*x-b);
+feas_old = inf;
+beta_1 = beta0/2;
+beta_tilde_1 = beta0/2;
+beta_tilde = beta0;
+k_t = 1;
+beta_old = beta;
+sigma_old = sigma;
+iter_const = zeros(maxit, 1);
+
+for ii = 2:maxit
+%         beta0_old=beta0;
+
+%     if feas_old <= beta0/sqrt(ii*log(ii+1)) && feas > beta0/sqrt(ii*log(ii+1)) 
+%         k0 = 1
+%         k_t = ii;
+% %         beta_1 = beta_old;
+%         beta_tilde_1 = beta;
+%         sigma_tilde_1 = sigma;
+%     end
+
+    betas(ii) = beta;
+    sigmas(ii) = sigma;
+%     if feas <= beta0/sqrt(ii*log(ii+1))
+% %         disp('beta1')
+%         beta = beta;
+%     else
+% %         disp('beta2')
+%         beta = beta * sqrt((ii*log(ii+1))/((ii-1)*log(ii)));
+%     end
+    
+%     if ii == k_t
+%         beta_tilde=beta;
+%     end
+%     if ii == 3
+%         beta1=beta;
+%     end
+    
+%     if k0 == 1 && ii == k_t
+%         beta1=beta;
+%     end
+% %     beta = beta0*sqrt(ii);
+    gamma = 1/(beta*LA);
+% 
+%     if feas <= sigma0/(ii*log(ii+1))
+% %         disp('sigma1')
+%         sigma = sigma;
+%     elseif feas > sigma0/(ii*log(ii+1)) && feas <= sigma0 /sqrt(ii*log(ii+1))
+% %         disp('sigma2')
+%         sigma = sigma * sqrt(((ii-1)*log(ii))/(ii*log(ii+1)));
+%     elseif feas > sigma0/sqrt(ii*log(ii+1))
+% %         disp('sigma3')
+% %         sigma = sigma0 * (beta - beta_old)/()
+% %         if ii == 2
+% %         sigma = sigma0/beta0 * (beta-beta_old);
+% %         else
+% % if ii == 2 
+% %     sigma = sigma0;
+% % else
+% % if k0 == 0
+% %     sigma = sigma0 * (beta-beta_old)/(beta0);
+%         sigma=sigma0*(beta-beta_old)/(beta_tilde-beta_tilde_1);
+% % else
+% %         sigma = sigma0 * (beta-beta_old)/(beta1-beta0);
+% % end
+% % end 
+% %         end
+%     end
+%     if isnan(sigma)
+%         keyboard
+%     end
+%     sigma = sigma0*sqrt(ii);
+    x = prox_l1(x - gamma*A'*(y + beta*(A*x-b)), gamma);
+%     sigma = 1e2*beta0/sqrt(ii);
+    feas = norm(A*x-b);
+    
+    [beta, sigma, k_t] = update_params(feas,feas_old, k_t, ii, beta_old, sigma_old, sigmas, betas, sigma0, beta0);
+    y = y + sigma * (A*x-b);
+
+    obj_vec_const(ii) = obj(x);
+    feas_const(ii) = norm(A*x-b);
+    iter_const(ii) = norm(x-x_org);
+    
+   feas_old = feas;
+       beta_old = beta;
+       sigma_old = sigma;
+
+end
+%%
+figure, loglog(betas), hold on, loglog(sigmas, '.-'), legend('beta', 'sigma');grid on;
+
+%% decreasing params
+
+LA = norm(full(A));
+
+beta0 = 1e1;
+beta = beta0;
+gamma = 1/(LA*beta);
+x0 = zeros(p, 1);
+x = x0;
+y0 = zeros(n, 1);
+y = y0;
+obj_vec_dec = zeros(maxit, 1);
+feas_dec = zeros(maxit, 1);
+iter_dec= zeros(maxit, 1);
+
+sigmas_dec=zeros(maxit, 1);
+betas_dec=zeros(maxit, 1);
+for ii = 1:maxit
+    beta = beta0*(ii);
+% beta=beta0;
+    gamma = 1/(beta*LA);
+    x = prox_l1(x - gamma*A'*(y + beta*(A*x-b)), gamma);
+    sigma = beta0;
+    sigma = beta;
+    y = y + sigma * (A*x-b);
+    
+    obj_vec_dec(ii) = obj(x);
+    feas_dec(ii) = norm(A*x-b);
+    iter_dec(ii) = norm(x-x_org);
+    sigmas_dec(ii)=sigma;
+    betas_dec(ii)=beta;
+end
+
+%%
+
+figure, subplot(131), loglog(abs(obj_vec_const-fopt)), hold on, loglog(abs(obj_vec_dec-fopt)), legend('adaptive', 'constant')
+subplot(132), loglog(feas_const), hold on, loglog(feas_dec), legend('adaptive', 'constant') 
+subplot(133), loglog(iter_const), hold on, loglog(iter_dec), legend('adaptive', 'constant') 
+
+
+
diff --git a/codes/convex_example_bp/update_params.m b/codes/convex_example_bp/update_params.m
new file mode 100755
index 0000000..5841c1f
--- /dev/null
+++ b/codes/convex_example_bp/update_params.m
@@ -0,0 +1,46 @@
+function [beta_, sigma_, k_t] = update_params(feas_cur, feas_old, k_t, iter, beta_old, sigma_old, sigma_vec, beta_vec, sigma_0, beta_0)
+% This function computes the parameters for the new iteration depending on
+% the predefined adaptive rule
+% INPUTS:  feas_cur: current feasibility value
+%          iter    : current iteration number
+%          sigma_0 : initial value for the dual step size
+%          beta_0  : initial value for the penalty parameter
+% OUTPUTS: beta_   : updated penalty parameter
+%          sigma_  : updated dual step size
+% 
+% Author: Mehmet Fatih Sahin
+% Date:   09.11.2018
+
+if iter<2
+    beta_ = beta_0;
+    sigma_ = sigma_0;
+    return
+end
+
+if feas_cur > beta_0/sqrt(iter)
+    beta_ = beta_old*sqrt(iter/(iter-1));
+else
+    beta_ = beta_old;
+end
+
+if feas_old <= sigma_0/sqrt(iter-1) && feas_cur > sigma_0/sqrt(iter) 
+    k_t = iter;
+end
+ 
+if feas_cur <= sigma_0/iter
+    sigma_ = sigma_old;
+elseif sigma_0/iter < feas_cur && feas_cur<=sigma_0/sqrt(iter)
+    sigma_ = sigma_old*sqrt((iter-1)/iter);
+else
+%     sigma_ = sigma_0/beta_0*(beta_-beta_old);
+    if k_t == iter
+        sigma_ = sigma_old/(beta_-beta_vec(k_t))*(beta_-beta_old);
+    elseif k_t == 1
+        sigma_ = sigma_0/beta_0*(beta_-beta_old);
+    else
+        sigma_ = sigma_vec(k_t)/(beta_vec(k_t+1)-beta_vec(k_t))*(beta_-beta_old);
+    end
+end
+        
+
+end
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