This method transforms an optimization problem with n variables and k constraints into an extreme value problem of a system of equations with n+k variables, and its variables are not subject to any constraints. This method introduces a new scalar unknown quantity, namely Lagrange multiplier: the coefficient of each vector in the linear combination of gradient of constraint equation.
Brief introduction of Joseph Louis Lagrange
Joseph-Louis Lagrange (173665438+1October 25th-1April 3rd 10), alias: Iosep Loevico Lagrange.
1755, he wrote a paper on minimax method, which developed the variational method initiated by Euler and laid a theoretical foundation for the variational method. 1756 was appointed as an academician of the prussian institute of communication. From 65438 to 0766, he was appointed as the Department of Mathematics of Prussia Academy of Sciences, and lived for 20 years, during which he completed the classic mechanical work Analytical Mechanics.
1772, "Three-body Problem" completed. In the same year, Fermat's other conjecture that Euler did not solve "a positive integer can be expressed as the sum of four squares at most" was proved. 18 1 1 year, and the equilibrium equation of elastic thin plate is deduced. 1783 was appointed honorary president of Turin Academy of Sciences. 179 1 was elected as a member of the royal society.
1795 Member of National Longitude Bureau. In the same year, he was elected chairman of the Mathematics and Physics Committee of the French Academy. 18 13 published the analytic function theory containing the main theorems of differential calculus. Without the concepts of infinitesimal, vanishing quantity, limit and flow number, the analytic function theory was reduced to the art of algebraic analysis and Lagrange's differential mean value theorem was obtained for the first time.