You can use the Taylor series expansion (geometrical series) of the first order in a neighborhood of any nonzero point x0:

1/x= 1/(x-x0+x0)=1/x0 * (1/(1+(x-x0)/x0)=1/x0 * (1-(x-x0)/x0+...)

being valid for all x close enough to x0, more precisely |x-x0|

Btissam, it is important what are you doing. Both mathematically and in application.

Taylor expansion is a formally correct approach. But why should you linearize? Important effect can occur in a point with large error. There is also nonlinear optimization, even in dynamic framework. See, for example, this paper (for math you can start from section 3): https://www.researchgate.net/publication/303689706_Economics_of_Talent_Dynamics_and_Multiplicity_of_Equilibria

Conference Paper Economics of Talent: Dynamics and Multiplicity of Equilibria

Hi, I agree with Yuri, it is not necessary to linearize the constraint in nonlinear programming. In addition if the constraint has the following form:

1/x*f(f)

Thank you all for your feedbacks.

The constraint I want to linearize is: sum(1/xi)