Minimization problem with multiple constraints
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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!
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Matt J
2017년 3월 3일
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?
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Matt J
2017년 3월 2일
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
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Matt J
2017년 3월 3일
편집: Matt J
2017년 3월 3일
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?
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