TITLE:
Solve the Polynomial Functions Conditional Extreme by Applying the Groebner Basis Method
AUTHORS:
Junyu Luo, Shengzhen Ding
KEYWORDS:
Groebner Basis, Polynomial Equations, Conditional Extremum
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.12 No.11,
November
25,
2022
ABSTRACT: In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the polynomial functions conditional extreme.
Firstly, we describe how to solve conditional extreme value problems by
establishing Lagrange functions and calculating the differential equations
derived from the Lagrange functions. Then, by solving the single variable
polynomials in the groebner basis, the solution of polynomial equations could
be derived successively. We overcome the high number of variables and
constraints in the extreme value problem. Finally, this paper illustrates the
calculation process of this method through the general procedures and examples
in solving questions of conditional extremum of polynomial function.