Validating Results
The LMI Lab offers two functions to analyze and validate the results of an LMI
optimization. The function evallmi
evaluates all variable terms
in an LMI system for a given value of the vector of decision variables, for instance,
the feasible or optimal vector returned by the LMI solvers. Once this evaluation is
performed, the left and right sides of a particular LMI are returned by showlmi
.
In the LMI problem considered in Minimize Linear Objectives Under LMI Constraints, you can verify that
the minimizer xopt
returned by mincx
satisfies the LMI constraint as follows.
evlmi = evallmi(LMIs,xopt) [lhs,rhs] = showlmi(evlmi,1)
The first command evaluates the system for the value xopt
of the
decision variables, and the second command returns the left and right sides of the first
(and only) LMI. The negative definiteness of this LMI is checked by
eig(lhs-rhs) ans = -2.0387e-04 -3.9333e-05 -1.8917e-07 -4.6680e+01