Maximum Eigenvalue Minimization

[jhzd...@gmail.com]

I am trying to determine whether it is possible to specify the
minimization of the maximum eigenvalue of a symmetric matrix in AMPL
where the goal is to solve for the matrix.

Specifically, my problem is of the form:
minimize ||A||_2
subject to Ax=b

where ||.||_2 is the matrix 2-norm, i.e. the maximum eigenvalue of A.
I have found references that via the Schur complement, this problem is
identical to:
minimize t
subject to Ax=b, [[tI, A], [A', tI]] >= 0
where this second constraint is saying that the block matrix is
positive semi-definite.

This is a standard problem that I have seen specified as a semi-
definite program in several sets of notes, but I do not know how it
can be specified in AMPL at all.

Anyone got any direction on that?

Thank you ahead of time for any help,

-Jesse

[Robert Fourer]

Dear Jesse,

Currently AMPL does not have support for this kind of semidefinite program.

Bob Fourer
4...@ampl.com

[Jesse Davis]

Thank you for the response Bob,
-Jesse