Use of fmincon with nonlcon inside a parfor loop

Hello,

I have the following code which is working fine... but slowly

for ii=1:9000
    fun = @p expression(p);
    wref=0;
    zref=1;
    loc_nlcon = @p nlcon(p,wref,zref);
    output=fmincon(fun,init,[],[],[],[],lb, ub,loc_nlcon);
end

function [c,ceq]=nlcon(p,w,z)
c=0;
ceq=z-expression(p,w);
end

I want to speed it up by using a parfor loop. However, as nlcon is a nested function, for loop cannot simply changed by a parfor one. By using an handle function (see below), my issue is that fcn returns only the first function parameter (c) and not both (c and ceq) as needed by fmincon. I am struggle finding the good solution to my problem.

parfor ii=1:9000
    fun = @p expression(p);
    fcn = @nlcon;
    wref=0;
    zref=1;
    output=fmincon(fun,init,[],[],[],[],lb, ub,fcn(p,wref,zref));
end

function [c,ceq]=nlcon(p,w,z)
c=0;
ceq=z-expression(p,w);
end

Thank you for your help.

Best

[Mike Croucher]

Could you post a fully working version of your slow code please?

[Matt J]

@Guilhem Pages You need to give a clearer description of the problem you are seeing. There is no problem with naively converting your original code to a parfor loop that I can see, other than that you are missing some parentheses,

parfor ii=1:9000   

    wref=0;
    zref=1;
    
    fun = @(p) expression(p,wref);   
    loc_nlcon = @(p) nlcon(p,wref,zref);
    
    output{ii}=fmincon(fun,init,[],[],[],[],lb, ub,loc_nlcon);
end

[Guilhem Pages]

@Mike Croucher, Thanks, I will do it later.

@Matt J, Thanks. using parfor the nested function cannot be used as with the for loop

[Matt J]

@Guilhem Pages Why does your nlcon function need to be nested? Your posted code isn't using any externally-scoped variables or other unique features of nested functions. Why not just make it a local function?

Answer 1

[Matt J]

Move the steps inside the loop to its own function doOptimization(). You can nest functions there, as in in the example below.

function main()

    N=10;
    output=cell(N,1);

    parfor i=1:10
      output{i}=doOptimization();
    end

end

function output=doOptimization

    fun = @(p) p.^2;
    wref=0;
    zref=1;

    [init,lb,ub]=deal(2,-1,4);

    loc_nlcon = @(p) nlcon(p,wref,zref);
    output=fmincon(fun,2,[],[],[],[],lb, ub,loc_nlcon);


    function [c,ceq]=nlcon(p,w,z) %nested
     c=0;
     ceq=z-(p.^2+w);
    end


end

[Guilhem Pages]

Thank you very much!!