On Types of Isolated KKT Points in Polynomial Optimization

Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝ n . In this paper, the authors 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, the...

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Veröffentlicht in:Journal of systems science and complexity 2023-10, Vol.36 (5), p.2186-2213
Hauptverfasser: Guo, Feng, Jiao, Liguo, Kim, Do Sang, Pham, Tien-Son
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Sprache:eng
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Zusammenfassung:Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝ n . In this paper, the authors 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, the authors investigate some properties of the tangency variety of f on S at x* , by which the authors introduce the definition of faithful radius of f over S at x* . Then, the authors 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, the authors propose an algorithm involving algebraic computations to compute a faithful radius of x* and determine its type.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-023-2119-7