solving non-linear systems inequalities

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I am trying to solve a non-linear systems of 14 inequalities with 12 variables, involving exponential and polynomial functions. I have been searching over the web for leads,but without any success.I know how to solve non-linear system of equations numerically. By solving I mean getting all feasible points.

So, what are the possible ways in which non-linear system of inequalities can be solved numerically?

Any links to text which discusses this issue would be great.