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 |
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| container_title | Journal of automated reasoning |
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| creator | Muñoz, César Narkawicz, Anthony |
| description | 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. |
| doi_str_mv | 10.1007/s10817-012-9256-3 |
| format | Article |
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| ispartof | Journal of automated reasoning, 2013-08, Vol.51 (2), p.151-196 |
| issn | 0168-7433 1573-0670 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | 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 |
| title | Formalization of Bernstein Polynomials and Applications to Global Optimization |
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