Lagrangian Multiplier with inequality constraints when variables has a matrix form

Hey Guys,

I am trying to implement the following optimization problem in MATLAB using the Lagrangian multiplier and got stuck at some points. Here is my code. Would anyone please be so kind as to help me to implement this correctly in MATLAB? Thanks in advance

the variable I am looking for is c with dimension of (I,L,K,M). The objective funcvtion is a function of R0 and R1 which each of these are a function of c.

ObjFun = f( R0(c), R1(c));
Const1 = sum(sum(c(:,:,:,:))) - 1 <= 0;
for k = 1 : K
    for m = 1 : M
        for l = 1 : L
            for i = 1 : I
                Const2 = -1*c(i, l, k, m) <= 0;
                Const3 = c(i, l, k, m) - 1 <= 0;
            end
        end
    end
end
LagrangianFun = ObjFun + lambda1*Const1 + lambda2*Const2 + lambda3*Const3;
dLagrangianFun_dc = diff(LagrangianFun,l) == 0; 
dLagrangianFun_dlambda1 = diff(LagrangianFun,lambda1) == 0; 
dLagrangianFun_dlambda2 = diff(LagrangianFun,lambda2) == 0; 
dLagrangianFun_dlambda3 = diff(LagrangianFun,lambda3) == 0; 
system = [dLagrangianFun_dc; dLagrangianFun_dlambda1; dLagrangianFun_dlambda2; dLagrangianFun_dlambda3]; 
[c_val, lambda1_val, , lambda2_val, lambda3_val] = solve(system, [c lambda1 lambda2  lambda3 ], 'Real', true) ;

[Susan]

the optimization problem is:

max_{c} \sum_{l}\sum_{i} f( R0_{i,l}(c), R1_{i,l}(c));

s.t. 0<= c(i, l, k, m) <= 1 for all k= {1, 2, ...., K} and m = {1, 2, ..., M} and i = {1,...., I} and l = {1,..., L}

sum_{l} sum_{i} c(i,l,k,m) <= 1 for all k= {1, 2, ...., K} and m = {1, 2, ..., M}

[Susan]

Any Suggestions?