Failure in initial objective function evaluation. LSQNONLIN cannot continue.

I am getting the LSQNONLIN error and I am hoping that someone can take a look at my objective function. I am sure I have written it completely wrong.

x will be an input vector of [rx ry rz mx my mz]. And what I would like to get out of this are the optimized values for [rx ry rz mx my mz].

G_measured calls a function that takes in a vector called Rmeasured and dipoleMoment and spits out data of 4x6 vector (4 measurement points measuring G elements), same with G_estimate.

Any help or guidance would be appreciated as I am fairly new to this.

options = optimoptions(@lsqnonlin);
options.Display = 'iter';
options.Algorithm = 'levenberg-marquardt';
options.StepTolerance = 1e-6;
options.MaxFunctionEvaluations = 1000;
x = lsqnonlin(@lm_obj,x_init, [],[],options)

x_init = [1, 3, 5, 10, 0, 10]
function F = lm_obj(x)
G_estimate = getGradientsEstimate(x);
G_measured = getGradientsMeasured(Rmeasured, dipoleMoment)
Difference = G_estimate - G_measured;
F = norm(Difference)
end   

[Ameer Hamza]

First, the correct orders of statements should be like this

x_init = [1, 3, 5, 10, 0, 10]; % initialized first
x = lsqnonlin(@lm_obj,x_init, [],[],options)

The error is caused by the functions getGradientsEstimate or getGradientsMeasured. How are they defined? What is the value of dipoleMoment, and where is it defined?

[sree chak]

Thanks for helping me with this. I did change the inputs of the getGradientsEstimate and getGradientsMeasured functions slightly. They are identical functions except the estimate function does not include noise.

Both functions sensorLoc ([x y z] position of a sensor), a targetLoc ([x y z] position of a target) and a dipoleMoment ([mx my mz] of a target). The outputs give us the five tensor elements [Gxx Gxy etc.] that are then subtracted and the error is formulated. The getGradientsEstimate instead of the targetLoc and dipoleMoment will taken in the x_init values.

getGradientsEstimate and getGradientsMeasured are defined in a separate m.files (within the same workspace) as the following:

function [G] = getGradientsEstimate(sensorLoc,targetLoc,dipoleMoment)
%Constants
mu = 4*10^(-7);
R = targetLoc - sensorLoc;
    r = norm(R);
    M_R = dot(dipoleMoment, R);
    %B = mu/(4*pi)*((3*M_R*R(i,:))/r^5 - dipoleMoment(i,:)/r^3);
    Gxx = mu/(4*pi)*((-15*M_R*(R(1,1))^2)/r^7 + 3*(2*dipoleMoment(1,1)*R(1,1) + M_R)/r^5);
    Gyy = mu/(4*pi)*((-15*M_R*(R(1,2))^2)/r^7 + 3*(2*dipoleMoment(1,2)*R(1,2) + M_R)/r^5);
    Gxy = mu/(4*pi)*((-15*M_R*R(1,1)*R(1,2))/r^7 + 3*(dipoleMoment(1,1)*R(1,2)+ dipoleMoment(1,2)*R(1,1))/r^5);
    Gxz = mu/(4*pi)*((-15*M_R*R(1,1)*R(1,3))/r^7 + 3*(dipoleMoment(1,1)*R(1,3)+ dipoleMoment(1,3)*R(1,1))/r^5);
    Gyz = mu/(4*pi)*((-15*M_R*R(1,2)*R(1,3))/r^7 + 3*(dipoleMoment(1,2)*R(1,3)+ dipoleMoment(1,3)*R(1,2))/r^5);
    G = [Gxx Gyy Gxz Gyz Gyz];
end

function [G] = getGradientsMeasured(sensorLoc,targetLoc,dipoleMoment)
%Constants
mu = 4*10^(-7);
%Gaussian Noise added individually to each tensor element
gradSigma = (50/3)*10^(-15); %based on the 100fT description in the data sheet
noise = gradSigma*randn(1);
R = targetLoc - sensorLoc
    r = norm(R);
    M_R = dot(dipoleMoment, R);
    %B = mu/(4*pi)*((3*M_R*R(i,:))/r^5 - dipoleMoment(i,:)/r^3);
    Gxx = mu/(4*pi)*((-15*M_R*(R(1,1))^2)/r^7 + 3*(2*dipoleMoment(1,1)*R(1,1) + M_R)/r^5) + noise;
    Gyy = mu/(4*pi)*((-15*M_R*(R(1,2))^2)/r^7 + 3*(2*dipoleMoment(1,2)*R(1,2) + M_R)/r^5)+noise;
    Gxy = mu/(4*pi)*((-15*M_R*R(1,1)*R(1,2))/r^7 + 3*(dipoleMoment(1,1)*R(1,2)+ dipoleMoment(1,2)*R(1,1))/r^5)+noise;
    Gxz = mu/(4*pi)*((-15*M_R*R(1,1)*R(1,3))/r^7 + 3*(dipoleMoment(1,1)*R(1,3)+ dipoleMoment(1,3)*R(1,1))/r^5)+noise;
    Gyz = mu/(4*pi)*((-15*M_R*R(1,2)*R(1,3))/r^7 + 3*(dipoleMoment(1,2)*R(1,3)+ dipoleMoment(1,3)*R(1,2))/r^5)+noise;
    G = [Gxx Gyy Gxz Gyz Gyz];
end

[Ameer Hamza]

getGradientsEstimate() needs 3 input variables, whereas you are only passing in one variable. I guess the vector x_init combines the value of sensorLoc, targetLoc, and dipoleMoment, but you need to split x vector into 3 variables and then pass it to these functions.