Algorithms for computing the global infimum and minimum of a polynomial function

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 is 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, the well-known Wu??s method plays an important role.