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This paper is devoted to the computation of distance to set, called , defined by polynomial equations. First we consider the case of quadratic systems. Then, application of results stated for quadratic systems to the quadratic equivalent of polynomial systems (see [5]), allows us to compute distance to semi-algebraic sets. Problem of computing distance can be viewed as non convex minimization problem: $d(u,S)={inf}_{x\in S}{\parallel x-u\parallel }^2$, where is in ${ℛ}^n$. To have, at least, lower approximation of distance, we consider the dual bound...