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Computation of the distance to semi-algebraic sets

Christophe Ferrier — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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 S x - u 2 , where is in n . To have, at least, lower approximation of distance, we consider the dual bound...

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