Global Minimization of a Multivariate Polynomial using Matrix Methods

Authors:
Bernard Hanzon;Dorina Jibetean
Affiliations:
Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. (e-mail: bhanzon@econ.vu.nl)/;Centrum voor Wiskunde en Informatica, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. (e-mail: d.jibetean@cwi.nl)
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

The problem of minimizing a polynomial function in several variables over Rn is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimal value and finds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm computes its infimum. No assumption is made on the polynomial.