Convert a MINLP problem with semi-continuous variables to a problem with continuous variables?

Question

Is there a way do (approximately) convert a nonlinear optimization problem with semi-continuous design variables to a problem with continuous variables? I want to avoid the use of MINLP solvers and instead go with my standard gradient-based solver I already have available for mechanical topology optimization applications. Maybe you know about some relaxation or penalization scheme, s.t. most of the optimal design variables fall into the feasible range $0$ or $[x_{\mathrm{min}},x_{\mathrm{max}}]$.