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 ...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.展开更多
基金supported by the Chinese National Natural Science Foundation under Grant No.11571350the Science and Technology Development Plan Project of Jilin Province,China under Grant No.YDZJ202201ZYTS302+1 种基金the National Research Foundation of Korea(NRF)Grant Funded by the Korean Government under Grand No.NRF-2019R1A2C1008672the International Centre for Research and Postgraduate Training in Mathematics(ICRTM)under Grant No.ICRTM012022.01。
文摘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.
