solve quadratic set of equations

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tilfani oussama
tilfani oussama 2018-8-20
编辑： Walter Roberson 2018-8-21
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
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tilfani oussama
tilfani oussama 2018-8-21
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 2018-8-21
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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tilfani oussama
tilfani oussama 2018-8-21
编辑：Walter Roberson 2018-8-21
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.
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tilfani oussama
tilfani oussama 2018-8-21
thank you for your reply, can you tell me more. Bests
Torsten
Torsten 2018-8-21
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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