B.1 Proof of Theorem 3.1
Proof. In order to find the Lagrange dual of problem (3.2), we first form the Lagrangian L as
L(p, q, [upsilon], [mu], [lambda], [gamma]) = -[p.sup.T] r - [[summation over (j)][q.sub.j] log [q.sub.j] + (q - [[P.sup.T]p).sup.T] + [mu](1 - [1.sup.T]p) + [p.sup.T][lambda] + [gamma](S - [p.sup.T] s) (B.1)
with Lagrange multiplier vector [upsilon] [member of] [R.sup.M x 1], Lagrange multiplier [mu], [gamma] [member of] R, and Lagrange multiplier ...