Supply linear constrain to optimizer

Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:

If the boundary cases were of interest it would be nice to have an
optimizer that allows linear inequality bounds (that is to optimize over a
simplex).

Anyone looking for a project? I don't actually think this is
particularly hard to do for someone who understands what the
box-constrained algorithm already does. (That is a nearly vacuous
statement, I know. Brian would be eligible, but hardly looking for a
project...). 

There are two approaches: Either allow the box to generalize into
arbitrary intersections of half-spaces (I don't think that's the
definition of a simplex?) , or allow linear *equality* restrictions to
be added to the original optimization problem, so that you could

max f(c1,c2,c3) subj. to 
c3 == c1 + c2
with constr.
0 < c1 < 1
0 < c2 < 1
c3 < 1

O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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