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Mixed-Integer Linear Programming problem

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NICOLO' DUCCINI on 9 Nov 2020
Edited: NICOLO' DUCCINI on 13 Nov 2020
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_solver sdpt3
variables x(n) y(n) binary;
maximize (sum(sum(rho*x)))
sum(y) == q;
sum(x) == 1;
sum(x) <= y';
x, y

Answers (1)

Pranav Verma
Pranav Verma on 12 Nov 2020
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.
  1 Comment
NICOLO' DUCCINI on 12 Nov 2020
Edited: NICOLO' DUCCINI on 13 Nov 2020
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)
But I did't obtain an appropriate result, maybe because there are some constraint problem, do you have some suggestion ?

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