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...
Gespeichert in:
Veröffentlicht in: | Journal of systems science and complexity 2023-10, Vol.36 (5), p.2186-2213 |
---|---|
Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
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 |