How can I solve the cvx problem wuth two variable

1

Q: One of the variables solved is almost zero,No matter how other variables are adjusted

q_UAV = 10;
q_car = 2;
Csingle_UAV = 1;
Csingle_car = 0.05;
C_req = 60;

cvx_begin
    variable K_UAV
    variable K_car
    minimize (K_UAV*q_UAV + K_car*q_car)
    subject to
    K_UAV*Csingle_UAV + K_car*Csingle_car >= C_req;
    K_UAV >= 0;
    K_car >= 0;
cvx_end
2

This is a very simple Linear Programing problem, which CVX and the solver it calls easily solves.

So you object to K_car coming out to be 0? That is a result of the model and input data. if Csingle_car is set to 0.25, then optimal K_car is 240, with optimal objective value 480; and if K_car is then also constrained to be equal to 0, the optimal objective value is 600, which is worse, thereby proving that K_car = 0 is not an optimal solution when Csingle_car is set to 0.25. Indeed, in this problem, K_car = 0 only becomes non-optimal (all other inputs being held constant) when Csingle_car is sufficiently large so as to make K_car = 0 not the best way of satisfying the first constraint, because it then makes non-zero K_car worth the non-zero contribution to the 2nd term of the objective, because of a more than offsetting saving to the first term of the objective, as made possible via the first constraint.

1 Like
3

Thank you. It’s helpful.