He, Jihuan A remark on Lagrange multiplier method. I. (English) Zbl 1096.49502 Int. J. Nonlinear Sci. Numer. Simul. 2, No. 2, 161-164 (2001). The author uses the Lagrange multiplier method to find stationary points of a function \(F(x,y)\) under the constraint \(g(x,y)=0\). The stationary points are obtained from the two equations \[ \frac{\partial F}{\partial x} - \frac{g_x}{g_y}\frac{\partial F}{\partial y}=0\text{ and }g(x,y)=0.\tag{A} \]He derives from these equations two other equations (B), where obviously (A) implies (B). The author gives examples when the converse it is not true and this is what he calls the “Lagrange crisis”. Reviewer: Ioan Bucataru (Iaşi) Cited in 2 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations Keywords:Lagrange multiplier; paradox; semi-inverse method PDF BibTeX XML Cite \textit{J. He}, Int. J. Nonlinear Sci. Numer. Simul. 2, No. 2, 161--164 (2001; Zbl 1096.49502) Full Text: DOI OpenURL References: [1] He J.H, Int. J. Turbo & 14 (1) pp 23– (1997) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.