What is a good way to adjust both parameters of a convex optimization problem?

Here is my matlab code, cvx objective function has two regularization parameters tau1 and tau2. I need to set appropriate tau1 and tau2 values to make re1 and re2 small enough (minimum would be best). I have tried many, many values, including using the for loop, but still can't get the best re1 and re2 results. Is there another way (e.g. intelligent algorithms) to find the right parameters? Thank you very much!

clc;clear
n = 128;
m = 64;
i_s = floor(m*0.05);
i_c = i_s;
x0 = zeros(n,1);
x10_spt = randperm(n);
x0(x10_spt(1:i_c)) = randn(i_c,1);
v0 = zeros(m,1);
v0_spt = randperm(m);
v0(v0_spt(1:i_c)) = randn(i_c,1);
Phi = 1/sqrt(m) * randn(m,n);
data = real(Phi * x0);
N = 200;
p = (1+data)/2;
s0 = rand(numel(data),N);
P = repmat(p,1,N);
s = P > s0;
s1 = sum(s,2);
s2 = s1/N;
edata = 2*s2-1;
y = edata + v0 ;
% these two parameters I need to tune, I have tried for loop, but can't get
% good results of re1 and re2
tau1=0.01; 
tau2=0.01;
% Recovery via CVX
cvx_begin quiet

variable x(n) ;
variable v(m);
minimize 0.5*pow_pos(norm(y - Phi * x - v),2) + tau1 * norm(x,1) + tau2 * norm(v,1);

cvx_end
re1 = norm(x - x0, 2)/ norm(x0, 2)
re2 = norm(v - v0, 2)/ norm(v0, 2)
% how to find the optimal tau1 and tau2,then re1 and re2 are minimum respectively

cvxr / CVX

What is a good way to adjust both parameters of a convex optimization problem? #26