On Types of Isolated KKT Points in Polynomial Optimization  

作　　者：GUO Feng JIAO Liguo KIM Do Sang PHAM Tien-Son 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]Academy for Advanced Interdisciplinary Studies,Northeast Normal University,Changchun 130024,China [3]Department of Applied Mathematics,Pukyong National University,Busan 48513,South Korea [4]Department of Mathematics,Dalat University,Dalat 96300,Vietnam.

出　　处：《Journal of Systems Science & Complexity》2023年第5期2186-2213,共28页系统科学与复杂性学报（英文版）

基　　金：supported by the Chinese National Natural Science Foundation under Grant No.11571350;the Science and Technology Development Plan Project of Jilin Province,China under Grant No.YDZJ202201ZYTS302;the National Research Foundation of Korea(NRF)Grant Funded by the Korean Government under Grand No.NRF-2019R1A2C1008672;the International Centre for Research and Postgraduate Training in Mathematics(ICRTM)under Grant No.ICRTM012022.01。

摘　　要：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.

关 键 词：Faithful radii KKT points polynomial functions tangency varieties TYPES 

分 类 号：O174.14[理学—数学]