Error : Failure in initial user-supplied nonlinear constraint function evaluation.

Hello everyone!

I'm encountering an issue with my MATLAB code and could use some assistance. Specifically, I'm getting the following error message:

[sol, fval, exitflag, output] = solve(prob);

Caused by:

Failure in initial user-supplied nonlinear constraint function evaluation.

It seems to be related to the evaluation of the nonlinear constraint function. I've attached the relevant part of my code below. I'm particularly confused because I linearised all my constraint terms, so I wasn't expecting any non-linearity.

Could you please help me identify the issue and suggest any potential fixes?

Thank you!

best Regards!

MyProblem()

Unrecognized function or variable 'N'.

Error in MyProblem (line 2)
A = optimvar('A', N, numNodes, Devices, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);

[Walter Roberson]

Variable N is not known.

[Maria]

Hello @Walter Roberson

N,numNodes,Devices are variables, we can set them (4,4,3) as example

[Walter Roberson]

N = 4;
numNodes = 4;
Devices = 3;
MyProblem()

Unrecognized function or variable 'tasks_generated'.

Error in MyProblem (line 5)
SR = sum(chi .* sum(tasks_generated, 2)) / sum(tasks_generated(:));

[Torsten]

We must be able to reproduce the error - otherwise we can't help.

Please add the missing routines @Walter Roberson listed to the code above and use the >RUN button to check whether the data and functions are complete.

[Walter Roberson]

We are missing:

• Compute_data_rate
• Compute_uplink_time_linear

Also, the lines

                            if dependency_matrix(k, prev_subtask, m) == 1
                                t_wait_aux >= Completion_Time(prev_subtask, prev_node, m) - uplink_time(k, n, m);
                            end

are not doing anything useful

[Maria]

@Walter Roberson i've used this

if dependency_matrix(k, prev_subtask, m) == 1
   t_wait_aux >= Completion_Time(prev_subtask, prev_node, m) - uplink_time(k, n, m);
end

because i have this non linear expression (max function)

[Torsten]

@Walter Roberson

I put all posted functions in the code above. It seems complete now.

[Walter Roberson]

t_wait_aux >= Completion_Time(prev_subtask, prev_node, m) - uplink_time(k, n, m);

calculates the result of the >= comparison, and assigns the result to the variable ans and surpresses display of ans because of the semi-colon.

Notice that you do not assign any output.

[Maria]

I found that it was the adequate expression to avoid use max function

[Walter Roberson]

It is a useless expression, because it does not assign to any output variable!

[Maria]

Does the issue come from this expression!!

[Torsten]

No. You just didn't set how t_wait_aux is defined.

Further, it's not necessarily true that setting

m >= x(1),m >= x(2),...,m >= x(n)

will give m = max(x) in an optimization. All values for "m" that are bigger than max(x) also satisfy the constraints.

It must be the case that "m" influences the objective function such that the lower its value the lower the value of the objective function (if your aim is to minimize). If this is the case, "m" will be chosen as max(x) by the optimizer.

Answer 1

[Walter Roberson]

            assigned_node = find(A(sb, :, v), 1);
          
            covering_uav = find(zeta_m_n(v, :), 1);
            
            if assigned_node == covering_uav

That code has a problem: assigned_node can come out empty. That leads to problems with the statement

                arg2_covering_to_assigned(k) = arg2(covering_uav, assigned_node, k)

as arg2() comes out empty when assigned_node is empty, but an empty result cannot be assigned to a definite output location.

When I add in some tracing lines, I get

no assigned node at v = 1, sb = 4, node = 1

no assigned node at v = 1, sb = 4, node = 2

no assigned node at v = 1, sb = 4, node = 3

no assigned node at v = 1, sb = 4, node = 4

no assigned node at v = 2, sb = 1, node = 1

no assigned node at v = 2, sb = 1, node = 2

no assigned node at v = 2, sb = 1, node = 3

no assigned node at v = 2, sb = 1, node = 4

repeated over and over again.

[Maria]

When i call find on A, it's looking for actual binary values (0 or 1), but since it's an optimization variable, it doesn’t contain concrete values until after the optimization is solved(that's why i used fcn2optimexpr).

Here is the reformulated SNR calculation without using find and instead directly express the SNR in terms of A.

function SNR_matrix = Compute_SNR(N, numNodes, Devices, A, zeta_m_n, h0, distances, alpha, RIS_elements, arg1, arg2, Theta_node, P_v, Noise_up)
SNR_matrix = optimexpr(N, numNodes, Devices);

for v = 1:Devices
    for sb = 1:N
        for node = 1:numNodes
            for node1 = 1:numNodes-1
                
                direct_SNR = sqrt(h0 * distances(v, node1)^(-alpha));
                direct_SNR = P_v * norm(direct_SNR)^2 / Noise_up;
               
                effective_power_sum = optimexpr(1);
                for k = 1:RIS_elements
                    effective_channel = Theta_node{node1} * arg1(v, node1, k) .* arg2(node1, node, k);
                    effective_power_sum = effective_power_sum + norm(effective_channel)^2;
                end
                ris_SNR = P_v * effective_power_sum / Noise_up;
                
                % Combine both contributions based on assignment and covering UAV
                SNR_matrix(sb, node, v) = A(sb, node, v) * (zeta_m_n(v, node1) * direct_SNR + (1 - zeta_m_n(v, node1)) * ris_SNR);
            end
        end
    end
end
end

[Torsten]

As far as I know, in an "fcn2optimexpr", you can do all computations as if they were numerical. So no need to define the two "optimexpr" for "SNR_matrix" and "effective_power_sum".

[Maria]

in this case i didn't use "fcn2optimexpr". I removed 'find' and i call the function as above .

[Torsten]

And the code works now ?

[Maria]

No, i'm still trying.

[Torsten]

Please supply the complete code you are using.

Are you sure to define SNR_matrix after computing it ?

SNR_matrix = Compute_SNR(N, numNodes, Devices, A, zeta_m_n, h0, distances, alpha, RIS_elements, arg1, arg2, Theta_node, P_v, Noise_up)
SNR_matrix = optimexpr(N, numNodes, Devices);

[Maria]

@Torsten it was just a mistake of copy paste, i already fixed it above.

[Torsten]

As said: we need the code to reproduce the error message in order to say anything.

[Maria]

Already fixed!

[Torsten]

Scroll through your constraints in the code above, and you will see that some of them cannot be fulfilled : they are of the form 0 = 1.

[Maria]

yes this is the problem, i didn't understand from where it comes 0.

[Torsten]

Data_rate must be an optimvar, not an optimexpr, I guess.

And be careful:

In the loop over i, it could happen that you assign conflicting constraints to Data_rate(sb, node, v).

Or you only want to assign an optimexpr to Data_rate(sb,node,v).

Then simply use

Data_rate(sb, node, v) = B_Uplink_MHz * (slope * SNR_matrix(sb, node, v) + intercept);

instead of imposing constraints:

prob.Constraints.(['approximation_', num2str(v), '_', num2str(sb), '_', num2str(node), '_', num2str(i)]) = ...
Data_rate(sb, node, v) == B_Uplink_MHz * (slope * SNR_matrix(sb, node, v) + intercept);

[Maria]

I did, but something went wrong.

[Torsten]

You must think about which equalities in your model are simple definitions of new variables and what are real constraints for optimization. I could bet that Data_rate(sb,node,v)=..., e.g., is a simple definition of a new variable as a combination of optimvars.

I changed the setting in the code above and MATLAB tells you that you got a nonlinear problem with equality constraints that ga cannot solve (besides other strange constraints of the form 0 <= 1).

[Maria]

I don't know if this can work, for example i solve nonlinear problem related to uplink time using fmincon and use the result to solve the original problem.

[Torsten]

I don't know if this can work, for example i solve nonlinear problem related to uplink time using fmincon and use the result to solve the original problem.

What do you mean by "this" ?

[Torsten]

I thought I could use different solvers to solve different parts of my problem, but it doesn't seem possible.

Usually it's possible, but I don't see an attempt where you try it in the code above.

And what is the problem with the code ? "intlinprog" claims having found the optimal solution.

[Maria]

There is no calculation done for SNR, Data rate and uplink time , so it was 0.

subject to uplinkConstraint:
       0 <= 0.3039
       0 <= 0.31376
       0 <= 0.40509

[Torsten]

If you define

Vehicle_Data = zeros(N, numNodes, Devices); % Ensure Vehicle_Data is defined

you automatically get uplink_time = 0, thus T_off = 0 and finally the constraints

subject to uplinkConstraint:
0 <= 0.3039
0 <= 0.31376
0 <= 0.40509

[Maria]

Yes i adjusted above.