Optimizing a Particular Real Root of a Polynomial by a Special Cylindrical Algebraic Decomposition

We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic decom...

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Bibliographic Details
Published inMathematics in computer science Vol. 5; no. 2; pp. 209 - 221
Main Authors Gandy, Silvia, Kanno, Masaaki, Anai, Hirokazu, Yokoyama, Kazuhiro
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.06.2011
Subjects
Computer Science
Mathematics
Mathematics and Statistics
Number-of-roots (NoR)-invariance
Primary 26C10
Cylindrical algebraic decomposition (CAD)
Optimization of a real root
Maximal real root
Secondary 49N05
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Summary:We study the problem of optimizing over parameters a particular real root of a polynomial with parametric coefficients. We propose an efficient symbolic method for solving the optimization problem based on a special cylindrical algebraic decomposition algorithm, which asks for a semi-algebraic decomposition into cells in terms of number-of-roots-invariance.
ISSN:1661-8270
1661-8289
DOI:10.1007/s11786-011-0090-5