fmincon for matrix optimization
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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!