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Mathematical optimization problem

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claudiocamera

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Hi, I am confused about the problem below:

Consider x* as the solution of :

minimize Σfi(xi) subject to Σxi=1 with xi ≥ 0 , i =1,2...,n

consider also that ζi= δfi(x*)/δxi, where δ represents the partial derivative operator.

Show that , there is a scalar k such that ζi≥k and (ζi-k)x*=0 , i= 1,2....n.

I appreciate any coments that lead me to solve this.
 

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