solve quadratic set of equations

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I have a system of equation which i would like to solven this systme can be expressed as :
w=(w1,...,wn)' and let consider a symmetric matrix n*n Σ(s), i would like to solve a system as :
ω(s) ω(s)’= inverse (Σ(s)).
can someone give a program/command to solve this kind of systems
  4 Comments
tilfani oussama
tilfani oussama on 21 Aug 2018
The amount of information would in both sides woul be n*(n-1)/2 as inverse Σ(s) and w * w' are both symmetric
Torsten
Torsten on 21 Aug 2018
Using w*w' for a vector w, you can only generate symmetric matrices of rank 1.
Your right-hand side is a matrix of rank n.
Believe us: Your system can't be solved for s unless n=1.
Best wishes
Torsten.

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Accepted Answer

tilfani oussama
tilfani oussama on 21 Aug 2018
Edited: Walter Roberson on 21 Aug 2018
Let me expose the problem from the beginning. My aim is to solve for w=(w1,...,wn)' an optimization problem, the probelm can be expressed as :
Max E(Rp(s))
subject to
k(s)=(ω(s)'Σ(s)ω(s))^(1/2)
e’ω(s) + υ(s) = 1
Let fix parameter s, and solve for one s value
Σ(s) = Ω(s) + σm2(s) β(s)*β(s)
β(s)=(β1(s),....,βn(s))'
and Ω(s) = diag(a1,...,an) with all elements are positives.
and
E(Rp(s)) = ω(s)c + ω(s)’β(s)Rm + υ(s)Rf
with Rm and Rf are knowns.
  3 Comments
tilfani oussama
tilfani oussama on 21 Aug 2018
thank you for your reply, can you tell me more. Bests
Torsten
Torsten on 21 Aug 2018
Just make an attempt to set up the problem for "fmincon" and come back if you encounter specific problems.
Best wishes
Torsten.

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