Linear Matrix Inequality

Specific Domains Optimization (Mathematical)
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A few comments:

  1. You do not have to build the huge matrix (function) by yourself - leave it up to the Convex.jl parser. Just create 6 constraints and then stack them into a vector of constraints.
  2. My remark from the original response still holds, you have not reacted to it. If P is a (matrix) variable, the second, third and fourth entries on the diagonal contain a product of P, hence your constraints are not linear.
  3. The fifth entry on the diagonal is irrelevant, it is just a constant matrix.
  4. But there is another problem with it: it is a product of P and P' scaled by a positive constant. No way to make it negative definite. Are you sure your problem statement is correct? In fact, this comment applies to some other components on the diagonal.
  5. Your matrices P1 through P5 in your code (or ∏₁ through ∏₅ in the above typeset math) are just scaled identity matrices. You can reduce the complexity of your formulas quite a bit by exploiting this knowledge about the structure of these matrices.

added later

  1. Semidefinite matrix variables (the matrix P in your case) are assumed symmetric in Convex.jl (and elsewhere, I bet). No need to perform tranposition then.
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