Optimization Relax Constraints

Question

I have got an optimization problem with a function to minimize and an equailty constraint. $$ min ~~f(x) \\ s.t. ~~~~~ h(x) = 1 $$ Now I am adding a penalty function $g(x)$ (which should be minimized, too) to $f(x)$ leading to $$ min ~~f(x) + µ g(x) \\ s.t. ~~~~~ h(x) = 1 $$which makes the problem non convex and solvebale for $x$. Becaus I do not care wheather $h(x)$ is excatly 1, I would like to ask, if there is a method to relax this constraint, eg. $0.2< h(x) < 1.8$, to make it easier to solve? Maybe a numeric one or a way to linearize it?