equality constraint

[mohmmed ahmed]

can you tell me what is the disadvantage of having equality constraint with LMIs

Example#1( LMI+with equality constraint)                        
         
PG==BZ
AX+A'X+P<0

Example#2(onlyLMI)
PG-BZ<0
AX+A'X+P<0

[Johan Löfberg]

There is  no disadvantage. If you want equality to hold, you must use an equality constraint.

(and the second model you have is not only an LMI. It is one LMI and a large amount if linear scalar inequalities since PG-BZ almost surely is a non-symmetric matrix)

[mohmmed ahmed]

thanks

can you tell me what do you mean by

[Johan Löfberg]

If you want PG to be equal to BZ (the equality to hold)