Unformatted text preview: z,x + 2 yz,2 xy + 3 z 21) . Therefore, critical points ( x,y,z ) can be identiﬁed with equation: 2 x + y2 z = 0 x + 2 yz = 02 xy + 3 z 21 = 0 Solving this, we get two group of solutions: (1 , , 1) and (1 / 3 , ,1 / 3) , which are the critical points of function f ( x,y,z ) . 2. The Hessian Matrix of f ( x,y,z ) is Hf ( x,y,z ) = 2 12 1 2121 6 z . For the ﬁrst critical point, the eigenvalues are 2 , 4√ 10 , 4 + √ 10 , which are all positive, therefore it is a local minimum point. For the second critical point, the eigenvalues are2 . 89 , 1 . 09 , 3 . 80 , therefore it is a saddle point. 1...
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 Spring '10
 Chan
 Critical Point, Optimization, hessian matrix

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