Starting point
As we mentioned, we need to start MCMCUMS with a valid .
Inversion of the dimensionreducing transformation
using pseudoinverse

(5.11) 
produces a solution for that meets the linear constraint
, but may have negativevalued elements.
A good initial starting point can be obtained from any
linearprogramming solver. Specifically, we find
the solution to the maximization of
subject to
It makes no difference
if we are maximizing or minimizing since is fixed
anyway by the linear constraints. Any linear programming (LP)
algorithm such as OCTAVE glpk.m or MATLAB linprog.m
can output a ``solution" which is a valid point.
See software/module_A_chisq_synth for additional details.
The best starting point, however, is the manifold centroid,
discused in Section 5.3.2.
Baggenstoss
20170519