Dear professor:
I have recently been dealing with state constraint with the expression as follows:
a’x + sqrt(a’Pa) <= b (1)
where the vector x and positive definite matrix P are decision variables, and a, b are constant vectors. In order to convex (1) without direct linearization, I introduce an augmented variable r, and transform (1) into following expression:
a’x + r<= b (2)
a’Pa - r^2 <=0 (3)
r > 0 (4)
I want to consult whether the expression (3) is convex and whether this transformation is appropriate.
Thank you very much.
