optimization of nested loop with two variables

I have an optimization problem of minimizing a two-stage sampling variance subject to the expected variable cost as constraint, and here are my functions:

the objective function is:

function dblSum=dblSumFun(n_h,m_hi)
h=length(N_h);
dblSum=0;
for h=1:length(N_h)
    iSum=0;
    for i=1:N_h(h)
        iTerm=(1/m_hi(i)-1/M_hi(i))*M_hi(i).^2*swh2(h);
        iSum=iSum+iTerm;
    end
    hTerm = (1/n_h(h)-1/N_h(h))*N_h(h)^2*sbh2(h)+N_h(h)/n_h(h)*iSum;
    dblSum=dblSum+hterm;
end
end

and the constraint is:

function [c,ceq]=nonlcon(n_h,m_hi)
h=length(N_h)
function dblSumc=dblSumFun(n_h,m_hi)
    dblSumc=0;
    for h=1:length(N_h)
        iSum=0;
       for i=1:N_h(h)
           iTerm=(0.5*m_hi(i))
           iSum=iSum+iTerm;
       end
        hTerm = 3.5-n_h(h)*0.7-n_h(h)/N_h(h)*iSum;
        dblSumc=dblSumc+hterm;
    end
end

ceq=dblSumc;% this will be satisfied if it eval to zero
c=[];

and the main coding for optimization is as follows

n_h0=zeros(length(N_h),1);%initial guess
m_hi0=zeros(26*n_h(h),1);
X0=[n_h0;m_hi0];

A=[];
B=[];

Aeq=[];
Beq=[];

options=optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed',...
    'MaxFunctionEvaluations',100000,'MaxIterations',2000,...
    'FunctionTolerance',1e-10);

[n_h,m_hi,const]=fmincon(@(n_h,m_hi) obj_function(n_h,m_hi),X0,A,B,Aeq,Beq,LB,UB,@(n_h,m_hi) nonlcon(n_h,m_hi),options)

I wanted to obtain a vector of n_h for h=1,...,26; and a vector of m_hi for h=1,...,26 and i=1,...,n_h(h). Any help?

Answer 1

[Amal Raj]

Hi Nilton, To obtain the vectors n_h and m_hi for your optimization problem, you can modify your code as follows:

% Define the objective function
objective = @(x) obj_function(x(1:length(N_h)), x(length(N_h)+1:end));

% Define the constraint function
constraint = @(x) nonlcon(x(1:length(N_h)), x(length(N_h)+1:end));

% Set initial guess
x0 = [n_h0; m_hi0];

% Set lower and upper bounds for variables
LB = [zeros(length(N_h), 1); zeros(26*sum(N_h), 1)];
UB = [inf(length(N_h), 1); inf(26*sum(N_h), 1)];

% Solve the optimization problem
x = fmincon(objective, x0, [], [], [], [], LB, UB, constraint, options);

% Extract the optimized values
n_h = x(1:length(N_h));
m_hi = x(length(N_h)+1:end);

In this code, the fmincon function is used to minimize the objective function obj_function subject to the constraint nonlcon. The initial guess x0, lower bounds LB, upper bounds UB, and optimization options options are also provided. The optimized values of n_h and m_hi are extracted from the solution vector x.