bi-linear terms in the objective function

[Vipin Pandey]

How can a bi-linear terms (multiplication of two decision variables ) in the objective function be transformed into a linear terms. Because, i tried to solve same problem using non-linear solver but it is taking too much time to solve the problem. it is to be noted there is no bilinear constraints. further the problem is being formulated as tri-level optimization. 

[Johan Löfberg]

if it a product of two continuous variables, it cannot be linearized (as per definition it is not linear, it is bilinear). You either solve it using a standard nonlinear solver, or a global bilinear solver, or approximate it using milp/sos2 approaches https://yalmip.github.io/command/interp2/