How to maximize this function: x1^2+x2^2+...+xn^2 ?

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Alex on 2 Jul 2012
How can I maximize the function x1^2+x2^2+...+xn^2
under some constraints which are LINEAR?
Thank you very much in advance!

Answers (2)

Sean de Wolski
Sean de Wolski on 2 Jul 2012
  1 Comment
Teja Muppirala
Teja Muppirala on 3 Jul 2012
Or how about QUADPROG?
H = identity matrix
f = zero vector
A,b = your linear constraints

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Richard Brown
Richard Brown on 3 Jul 2012
Edited: Richard Brown on 3 Jul 2012
I assume you mean minimise rather than maximise, because unless you have n independent constraints, your problem is unbounded.
In this case, assuming your constraints are Ax = b, just use the QR factorisation
[Q, R] = qr(A', 0);
x = Q * (R' \ b);
  1 Comment
Richard Brown
Richard Brown on 3 Jul 2012
just reread your question - if your constraints are inequalities, quadprog is the way to go

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