On types of KKT points in polynomial optimization
Abstract
Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in Rn. In this paper, we are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point x* of f over S. To this end, we investigate some properties of the tangency variety of f on S at x*, by which we introduce the definition of faithful radius of f over S at x*. Then, we show that the type of x* can be determined by the global extrema of f over the intersection of S and the Euclidean ball centered at x* with a faithful radius. Finally, we propose an algorithm involving algebraic computations to compute a faithful radius of x* and determine its type.
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