fmincon for matrix optimization

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yp78 on 23 May 2019
Commented: yp78 on 24 May 2019
I am trying to solve the following minimization problem:
  • where the is a positive number, Wis a 11-by-3 orthogonal (eigenvector) matrix, and Ω is the 3-by-3 diagonal (eigenvalue) matrix
  • the free parameters to be optimized are the last column vector (11-by-1) of W, and the last eigenvalue (1-by-1 schaler) in Ω.
Subject to the constraints:
  • .
I am looking at fmincon, but the problem seems to be not as straight forward as I initially thought. Below is my wroking code.
In particular, I want to know:
1. whether the following structure is correct
2. how to make "myObjectivefunction" to optimise the vector and scaler values at the same time
optimized = fmincon(@(x) myObjectivefunction, initialV,[],[],w',beq,[],[],@nonLinconVec,options);
  • optimized is a 12-by-1 vector of outputs. I put the eigenvalue in the first element, and the eigenvector in to (2:end) of the vector (not sure if it's correct or not)
  • [w', beq] satisfies the first constraint (verified)
  • @nonLinconVec: a separate file for the second constraint (verified)
I truly appreciate your help and suggestions!
yp78 on 24 May 2019
Hi Matt, thanks to your comments, I become aware of the problem. I started to reform the optimization problem from different perspective now.

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