i need find an expression in terms of(adsbygoogle = window.adsbygoogle || []).push({}); vfor the minimum value of(x^t)xsubject to the constraint(v^t)x= k

v is a fixed vector in R^n

k is a real constant

I need to use langrange multitpliers to solve this.

My solution

I letL(x,lambda) =(x^t)x + lambda*(k - (v^t)x)

so thereforegrad L = 2x - lambda*v = 0

so i therefore letx = 1/2*lambda*vand put this into the constraint to get

(v^t)*1/2*v*lambda = k

so1/2*lamda*(v^t)*v = kin terms ofv

To verify this is the min, i differentiated grad L again to get 2 >0 so this is convex and hence a global minimizer.

Prohlem

Can some one please check my solution, i was getting whether to differentiate with respect tovas well as it is a vector, but wasnt too sure?.. if some one can give me some advise that would be great thanks

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# Homework Help: Langrange multipliers - check my soluton please

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