I have an optimization problem with bilinear terms in the objective function and constraints, formulated as below:

$ \min C_1 x_1y +C_2 x_2y + C_3 x_3y$

subject to:

$z_1 + (A-1) x_1 y + A x_2 y + ...+ A x_Ny \leq B $

$z_2 + A x_1 y + (A-1) x_2 y + ...+ A x_Ny \leq B $

$z_m + A x_1 y + A x_2 y + ...+ (A-1) x_Ny \leq B $

$x_2 + \alpha < D $

$y + \beta < F $

where $A = 1/N$ and $z$, $x_n$, $z_m$, $\alpha$, $\beta$ and $y$ are unbounded decision variables. $A$ is a positive parameter between $0<A<1$.

Is there any way to reformulate the above into a SDP or other convex problem, or am I restricted to a non-linear optimization in this case?

Many thanks


It’s just linear with $u_i=x_iy \ \forall i$.

  • $\begingroup$ Apologies I should have mentioned that $x_i$ and $y$ are separately involved in other linear constraints in the formulation. I have edited the problem statement above. $\endgroup$ Oct 21 '20 at 0:14
  • $\begingroup$ @Fenderman2014 Same answer! $\endgroup$
    – Khue
    Oct 21 '20 at 0:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.