What should I do when fmincon returns exit flag -2 for all voxels?

Hi all, I'm having troubles using fmincon to fit the function below:

function [out] = sm_signal_high(bvalues, Sig_high, perp, delta_lambda)
% bvalues and Sig_high are Nx1 column vectors.
% perp and delta_lambda are both scalars.
sig_high = exp(-bvalues*perp).*sqrt(pi./(4*bvalues*(delta_lambda))).*erf(sqrt(bvalues*(delta_lambda)));
out = sum((Sig_high - sig_high).^2);
end

For all voxels that are being fit, I'm receiving an exit flag of -2 meaning that no feasible point was found. What exactly does this mean? How can I resolve this issue? Here is the code that I have written to perform this:

lambda_perp = zeros(X, Y, Z);
deltaLambda = zeros(X, Y, Z);
opts = optimset('Display', 'off');
lambdas0 = [0.60e-4, 1.30e-3];
exit_flags_high = zeros(X, Y, Z);
for z = 1:Z % For every particular voxel...
    for y = 1:Y
        for x = 1:X
            % As I am commenting this code for readability, I noticed it would be 
            % more efficient to write mask(x, y, slices(z)) == 1 since all 
            % values are by default 0. I'll change this later.
            if mask(x, y, slices(z)) == 0 % Set all values outside of the mask to be 0.
                lambda_par(x, y, z) = 0;
                lambda_perp(x, y, z) = 0;
                deltaLambda(x, y, z) = 0;
            else
                S_high_avg_formatted = zeros(high_num_unique, 1); % Reformat the average signal within a voxel.
                for b = 1:high_num_unique % Vectorize eventually!!!
                    S_high_avg_formatted(b, 1) = S_avg_high(x, y, z, b);
                end
                
                % high_unique and S_high_avg_formatted are Nx1 column
                % vectors. lam(1) and lam(2) are scalars representing
                % lambda_perp and deltaLambda respectively.
                [lambdas, ~, exit_reason_high, ~] = fmincon(@(lam) sm_signal_high(high_unique, S_high_avg_formatted, lam(1), lam(2)), ...
                         lambdas0, [], [], [], [], [0.40e-4, 0.92e-4], [0.80-4, 1.76e-3], [], opts);
                % The bounds of our fit have been determined by biological constraints.
                % ERROR: The function isn't actually fitting anything? It returns the values of lambda0 for all
                % particular voxels.
                
                % From lambdas, determine the eigenvalues within a particular voxel.
                lambda_perp(x, y, z) = lambdas(1);
                deltaLambda(x, y, z) = lambdas(2);
                
                exit_flags_high(x, y, z) = exit_reason_high;
            end
        end
    end
end

I'm aware that lsqcurvefit would perform a similar fitting and have already implemented that in a different script, however I wanted to try the different fitting algorithm to see if that would make a difference. Thank you!

-Warren

[Warren Boschen]

Turning off opts reveals the following message:

Exiting due to infeasibility:  1 lower bound exceeds the corresponding upper bound.

What does this mean exactly? My bounds are set correctly unless I'm missing something incredibly obvious.

Answer 1

[Warren Boschen]

I was missing something incredibly obvious. I had an upper bound written as 0.80-4 instead of 0.80e-4.