sci.op-research

On Nov 14, 6:08 am, marko.suonp...@24net.zzn.com wrote:
> Is it easy to include restriction that only one of two variables in LP
> problem can be > 0? There would be many such pairs. Currently I am
> using revised simplex to solve the problem, but obviouslly without the
> mentioned restriction.
>
> Br, Marko

Since no else has mentioned it, I'll suggest that the original poster
look into the subjects of "Linear Complementarity Problems" and
"Mathematical Programs with Equilibrium Constraints." These classes
of problems include the kinds of complementarity constraints mentioned
in the original posting.

It's possible that the original poster's problem is or can be put into
the form of an LCP:

Given an matrix n by n matrix M and an n element vector w, find
vectors q and w such that

q=w-Mz
x_i * z_i = 0 i=1, 2, ..., n
w>=0
z>=0

LCP's are not linear programming problems and most LP software can't
solve LCP's, but there are other specialized algorithms for the
solution of LCP's.

There's also been a lot of interest in recent years in modeling and
algorithms for mathematical programs with equilibrium constraints
(MPEC). This class of problems includes LCP's but is much more
general. Algorithms for the solution of MPEC are a topic of current
research interest.

Brian Borchers
Department of Mathematics
New Mexico Tech
Socorro, NM 87801