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In my two-stage continuous NLP problem, I have a constraint in second stage:

$X_{g,k}$ = $X_{g,0} + a_{g} d_{g} $, if $X_{g,k} \in [X_g^u,X_g^l]$

$X_{g,k} = X_g^u$, if $X_{g,k} \geq X_g^u$

$X_{g,k} = X_g^l$, if $X_{g,k} \leq X_g^l$

Here $a_{g}$ is a predefined factor between {0,1}, and $d_{g}$ is an unbounded variable. $X_{g,0}$ is a first-stage value of variable $X_{g,k}$. It can be implemented using two binary variables but I want to keep the problem continues for efficient computation. How can I handle such constraints?

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