how to solve the following problem using optimization toolbox?

I have this estimation problem where I use maximum likelhood estimation to solve it where the problem has pdf of:

 f(x)=m1*(1/(sqrt(2*pi)*o_x)))*exp(-0.5*power(z-ux,2)/o_x^2))+(1-m1)*m1*(1/(sqrt(2*pi)*o_y)))*exp(-0.5*power(z-uy,2)/o_y^2));

both are normal distributions (I want to estimate m1, ux,uy,o_x,o_y) using optimisation toolbox

I used fmincon since I am trying to limit the range of possible values (impost constraints on the values of m1, ux,uy,o_x,o_y)

I used a for loop for the main program.

problem.objective = @(y)norm_likelhood_fun(y,z); %%%%z is the data and y is a vector representing vector of values to be estimated
for j=1:100
% problem.x0=(problem.ub+problem.lb)/2;
problem.x0 = rand(5,1);
 [y,feval]=...
 fmincon(problem);
%y = run(gs,problem);
y_f(:,j)=y;
end

In each loop iteration, different initial values are used to search for minumum( I know the optimiser is sensitive to initial values). My question is how can I reach the convergence (different initial values lead to the same solution). What is the best algorithm suited for this problem?. How can I visualize the data with optimisation problem I have (contour lines)?

[Mario Malic]

Provide information on full problem structure, including lb and ub. I am not sure if you need them vectorised/or if it has any benefits in fmincon or just for simplicity.

Values for x0 are in range of [0,1]? Keep in mind, that fmincon is local search, you might end up in one or the other local minima.

[Muna Tageldin]

o

options = optimoptions('fmincon','Display','iter','Algorithm','sqp','MaxIter',10000,'TolX',10^-30,'TolFun',10^-30,'StepTolerance',1e-3);
problem.options = options;
problem.x0 = rand(5,1);
problem.nonlcon = [];
problem.A = []; 
problem.b = [];
problem.Aeq = [];
problem.beq = [];
problem.lb = [1e-6 1e-6 1e-6 1e-6 1e-6];
problem.ub = [0.99 0.99 0.99 0.99 0.99];

[Muna Tageldin]

whats the best way to visualise the optimisation problem (local and global minumum)?

[Mario Malic]

I don't think it's possible, it's 5D problem. Do you really need 10^-30 on TolX and TolFun?

Issue with your options are, that your MaxIter, TolFun and TolX are from optimset, but you use optimoptions. I don't know what values you get in fval (rename from feval, as feval is a function), so try these options.

options = optimoptions('fmincon','Display','iter-detailed','Algorithm','sqp','MaxIterations',10000, ...
    'StepTolerance',10^-10,'TolFun',10^-10,'OptimalityTolerance',1e-12, 'Plotfcn', @optimplotfval);