An MINLP from a paper I am reading has the following expression in its constraints:
Where from left to right:
$p_{l,s}$: continuous variable
$z_l$: binary variable
$b_l$: constant
$\Delta \theta_{l,s}$: continuous variable
$\lambda_l$: binary variable
$u_l$: binary variable
The authors of this paper replaces the second term with a continuous variable $\zeta$ as shown here:
The authors then mention:
By substituting this new variable for the third order polynomial, we are lifting the third order polynomial equation into a higher dimensional space and overcoming its nonlinearity.
What does that mean? what does overcoming the nonlinearity mean in this context?