## Lagrangian Multiplier with inequality constraints when variables has a matrix form

### Susan (view profile)

on 18 Apr 2019
Latest activity Commented on by Susan

### Susan (view profile)

on 19 Apr 2019
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

### Susan (view profile)

on 18 Apr 2019
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

on 19 Apr 2019
Any Suggestions?