## Minimization problem with multiple constraints

### chayma chaabani (view profile)

on 2 Mar 2017
Latest activity Edited by Matt J

### Matt J (view profile)

on 3 Mar 2017
I am trying to minimize the following objective function obj(x) = 1 - x*T where x is a 1 dimensional variable and T is a matrix. I have two constraints :
1) x should be positive : x>0
2) The objective function should be positive : 1-x*T>0 so x should be smaller than the minimum of all the matrix inverse values x < min(1/T).
I am not really familiar with Matlab optimization tools and I don't know which Matlab optimization function is adequate for this problem. Would you please give me some recommendations and advice.
Thank you!

Torsten

### Torsten (view profile)

on 3 Mar 2017
How do you define "the minimum return matrix" ?
Best wishes
Torsten.
chayma chaabani

### chayma chaabani (view profile)

on 3 Mar 2017
In my case, all the values of the return matrix should be minimal.
Matt J

### Matt J (view profile)

on 3 Mar 2017
But multiple functions of x cannot necessarily reach there minima simultaneously at the same x. What is it about your "case" that makes this possible?

### Matt J (view profile)

on 2 Mar 2017

See my comments, butI suspect the answer you are looking for is x=min(1/T). This simultaneously minimizes all entries of the matrix-valued function 1-T*x

chayma chaabani

### chayma chaabani (view profile)

on 3 Mar 2017
Unfortunately x=min(1/T) can't be a solution because in this case I will have zero values in the final minimum matrix of the objective obj(x) = 1 - x*T. The objective function should be strictly positive.
Matt J

### Matt J (view profile)

on 3 Mar 2017
The objective function should be strictly positive.
Then you have more work to do on the problem formulation, as there is currently nothing in what you've posed that ensures this.
Suppose T=ones(N). Then clearly the solution has to be x=1 and obj(x)=zeros(N). If this is not the solution for such a selection of T, then what is?