Computing global minima to polynomial optimization problems using Gröbner bases
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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.
Key wordsGlobal optima Gröbner bases polynomial optimization problems
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