Thread: minimum value subject to the constraint

Hi i was wondering if anyone can help me with this problem.. i was thinking of using Lagrangian's multipliers method to solve this., but i alsos get confused with transpose part i.e. (^t)

i need to find an expression in terms of s for the minumum value of (x^t)x subject to the constraint (s^t)x = k

s is a fixed vector in R^n
k is a real constant

and i also need to justify this is a minimum

if anyone can help..that would be great thanks

Originally Posted by dopi

Hi i was wondering if anyone can help me with this problem.. i was thinking of using Lagrangian's multipliers method to solve this., but i alsos get confused with transpose part i.e. (^t)

i need to find an expression in terms of s for the minumum value of (x^t)x subject to the constraint (s^t)x = k

s is a fixed vector in R^n
k is a real constant

and i also need to justify this is a minimum

You don't need Lagrange multipliers, it's just simple algebra!

, and therefore . But . So the minimum value of is , and it occurs when .

Hi thanks for the reply..however as i am learning about lagrangian multipliers and kuhn tucker methods, i sujested using langrangian method, so then i could use hessian matrix to justify my minimum, by checking the leading minor principles. Like i said when i expand or differentiate equations with the the transpose sign,,..i get confused where to put the t.

But with what you have shown i dont know how to justify the minumum..any suggestions??