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 (Equation 4-10) 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
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