By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper...By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.展开更多
In a recent article,the authors provided an effective algorithm for both computing the global infimum of / and deciding whether or not the infimum of / is attained,where / is a multivariate polynomial over the field R...In a recent article,the authors provided an effective algorithm for both computing the global infimum of / and deciding whether or not the infimum of / is attained,where / is a multivariate polynomial over the field R of real numbers.As a complement,the authors investigate the semialgebraically connected components of minimum points of a polynomial function in this paper.For a given multivariate polynomial / over R,it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of / whenever /has its global minimum.展开更多
基金partially supported by National Natural Science Foundation of China (Grant Nos. 10761006, 11161034)
文摘By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.
基金supported by the National Natural Science Foundation of China under Grant No.11161034the Science Foundation of the Education Department of Jiangxi Province under Grant No.Gjj12012
文摘In a recent article,the authors provided an effective algorithm for both computing the global infimum of / and deciding whether or not the infimum of / is attained,where / is a multivariate polynomial over the field R of real numbers.As a complement,the authors investigate the semialgebraically connected components of minimum points of a polynomial function in this paper.For a given multivariate polynomial / over R,it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of / whenever /has its global minimum.
