I encounter some problems when using using the Dinkelbach method

1

The issue I want to solve is as follows:
max (log2(2-2/(x+2))+log2(2-2/(y+2)))/(x+y)
s.t. x>=0, y>=0, x+y<=50
And I’m trying to solve it with the Dinkelbach alghorithm, my code is as follows:

clc,clear;
close all;

eps=0.000001; %Convergence condition
iter_max = 30; %itewration steps
x = zeros(1,iter_max+1);
y = zeros(1,iter_max+1);
r = zeros(1,iter_max+1); %initialize
x(1) = 0;
y(1) = 0; %Set the value of the first step to 0
r(1) = rand(1); %Set the initial value of the function to a random value

for iter=1:iter_max %start
% update x&y
cvx_begin quiet
variables x1 y1
maximize (((log(2-2/(x1+2))/log(2))+(log(2-2/(y1+2)/log(2))))-r*(x1+y1)) %function after the Dinkelbach transformation
subject to
x1>=0;
y1>=0;
x1+y1<=50;
cvx_end
x(iter+1)=x1;
y(iter+1)=y1;

% Judgment of convergence & upadte r
if cvx_optval <= eps %stop if it converges
break
else
r(iter+1) = (((log(2-2/(x(iter+1)+2)))/log(2))+(log(2-2/(y(iter+1)+2)/log(2))))/(x(iter+1)+y(iter+1)); %update r if not convergence
end

end
figure
plot(r(1:iter),‘b-o’,‘linewidth’,1.5);
grid on
xlabel(‘iteration number’)
grid on
box on
ylabel(‘objective value’);

I keep getting an error when I run the code, and it says like this:

Error using ./ (line 42)
Disciplined convex programming error:
Invalid operation: {2} / {real affine}

Error in / (line 17)

Error in formal_test (line 17)
maximize (((log(2-2/(x1+2))/log(2))+(log(2-2/(y1+2)/log(2))))-r*(x1+y1)) %function after the Dinkelbach transformation

I’m a beginner in CVX and don’t know how to fix this, can you please explain how to solve this problem?
Thanks!

2

help inv_pos

inv_pos Reciprocal of a positive quantity.
inv_pos(X) returns 1./X if X is positive, and +Inf otherwise.
X must be real.

 For matrices and N-D arrays, the function is applied to each element.

  Disciplined convex programming information:
      inv_pos is convex and nonincreasing; therefore, when used in CVX
      specifications, its argument must be concave (or affine).
3

Thanks for your answer, the question about “{real affine}” seems to have been solved, but I’ve run into a new problem, The error message is as follows:

Error using formal_test (line 22)
Your objective function is not a scalar.

I’ve tried setting the variables x1 and y1 to a one row and one column matrix (setting them as scalars), but still can’t solve it, can you please explain how to solve this problem?
Thanks!

4

If you insert the objective function in the program just before the maximize statement, what does it say? I.e., type the objective function, but without maximize. if that is not a real scalar, you will get an error message, because objective function needs to evaluate to a real scalar.

Perhaps you are missing one or more levels of sum, or need an inner product to produce a scalar, or incorrectly declared variables, or incorrectly produced input data. It is your problem, not mine, so I have no idea what the correct resolution is. I don’t even know what program and input data you ran which produced this error message.