Computing global minima to polynomial optimization problems using Gröbner bases
暂无分享,去创建一个
The local optimality conditions to polynomial optimization problems are a set of polynomial equations (plus some inequality conditions). With the recent techniques of Gröbner bases one can find all solutions to such systems, and hence also find global optima. We give a short survey of these methods. We also apply them to a set of problems termed ‘with exact solutions unknown’ in the problem sets of Hock and Schittkowski. To these problems we give exact solutions.
[1] Mokhtar S. Bazaraa,et al. Nonlinear Programming: Theory and Algorithms , 1993 .
[2] Donal O'Shea,et al. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.
[3] Klaus Schittkowski,et al. More test examples for nonlinear programming codes , 1981 .
[4] Stephen R. Czapor,et al. Solving Algebraic Equations: Combining Buchberger's Algorithm with Multivariate Factorization , 1989, J. Symb. Comput..