  In part I of this two-part work, certain minimization problems based on a
parametric family of relative entropies (denoted $\mathscr{I}_{\alpha}$) were
studied. Such minimizers were called forward
$\mathscr{I}_{\alpha}$-projections. Here, a complementary class of minimization
problems leading to the so-called reverse $\mathscr{I}_{\alpha}$-projections
are studied. Reverse $\mathscr{I}_{\alpha}$-projections, particularly on
log-convex or power-law families, are of interest in robust estimation problems
($\alpha >1$) and in constrained compression settings ($\alpha <1$).
Orthogonality of the power-law family with an associated linear family is first
established and is then exploited to turn a reverse
$\mathscr{I}_{\alpha}$-projection into a forward
$\mathscr{I}_{\alpha}$-projection. The transformed problem is a simpler
quasiconvex minimization subject to linear constraints.
