Mixed-Integer Linear Programming problem

Hello,

i have to solve the following MILP problem on MATLAB:

I have tried to solve it in this way, but there is something wrong because the are not solutions according to the solver but there should be 2 vectors with 4 solutions each. Can anyone help me?

q = 4
n = length(tickers)

cvx_begin
cvx_solver sdpt3
variables x(n) y(n) binary;
maximize (sum(sum(rho*x)))
sum(y) == q;
sum(x) == 1;
sum(x) <= y';
cvx_end
x, y

Answer 1

[Pranav Verma]

Hi Nicolo'

You can use the MILP solver in MATLAB to solve the problem you have mentioned. The MILP solver solves:

So make sure that you convert your problem from maximize to minimize and accordingly change the signs in the constraints and convert them to A.x <= b.

You can make use of optimproblem to create the optimization problem.

Thanks

[NICOLO' DUCCINI]

Thank You for your answer!

I tried to modify the code in this way:

prob = optimproblem('ObjectiveSense','max')
x = optimvar('x',n,'Type','integer','LowerBound',0,'UpperBound',1);
y = optimvar('y',n,'Type','integer','LowerBound',0,'UpperBound',1);

prob.Objective = optimexpr(rho*x);
cons1 = sum(y) == q;
cons2 = sum(x) == 1;
cons3 = x <= y'*ones(30,1);
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;
sol = solve(prob)

sol.x
sol.y

But I did't obtain an appropriate result, maybe because there are some constraint problem, do you have some suggestion ?