inv_pos((p2*g + s)*rel_entr(p2*g + s, p1*g + p2*g + s)
simplifies to
log((p2*g + s)/(p1*g + p2*g + s))
which is neither convex nor concave. So I believe the first constraint, and therefore the optimization problem, are not convex,
inv_pos((p2*g + s)*rel_entr(p2*g + s, p1*g + p2*g + s)
simplifies to
log((p2*g + s)/(p1*g + p2*g + s))
which is neither convex nor concave. So I believe the first constraint, and therefore the optimization problem, are not convex,