Formalization of Bernstein Polynomials and Applications to Global Optimization

This paper presents a formalization in higher-order logic of a practical representation of multivariate Bernstein polynomials. Using this representation, an algorithm for finding lower and upper bounds of the minimum and maximum values of a polynomial has been formalized and verified correct in the...

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Veröffentlicht in:	Journal of automated reasoning 2013-08, Vol.51 (2), p.151-196
Hauptverfasser:	Muñoz, César, Narkawicz, Anthony
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Artificial Intelligence Automated reasoning Computer Science Exact sciences and technology Logic Logic and foundations Mathematical Logic and Formal Languages Mathematical Logic and Foundations Mathematical logic, foundations, set theory Mathematics Optimization Proof theory and constructive mathematics Prototypes Representations Sciences and techniques of general use Strategy Symbolic and Algebraic Manipulation Upper bounds
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Beschreibung
Zusammenfassung:	This paper presents a formalization in higher-order logic of a practical representation of multivariate Bernstein polynomials. Using this representation, an algorithm for finding lower and upper bounds of the minimum and maximum values of a polynomial has been formalized and verified correct in the Prototype Verification System (PVS). The algorithm is used in the definition of proof strategies for formally and automatically solving polynomial global optimization problems.
ISSN:	0168-7433 1573-0670
DOI:	10.1007/s10817-012-9256-3