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A remark on Lagrange multiplier method. I. (English) Zbl 1096.49502

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”.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
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References:

[1] He J.H, Int. J. Turbo & 14 (1) pp 23– (1997)
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