sci.op-research

The number of a_k's is within the range of 100-1000 variables. The x_i
are similarly in the same range. That's why explicit enumeration does
not work and I am looking for a cheap yet not too rough approximation
for complementarity constraints.

As we discussed, the complementarity can be encoded through bilinear
terms which are not convex. I personally prefer a convex relaxation as
opposed to using a non-convex solver, because I dislike that the
quality of solution depends on an initial guess!

G.D.

On Feb 27, 1:28=A0am, Johan L=F6fberg wrote:
> golabid...@gmail.com wrote:
> > Thank you for connecting complementarity constraints to a larger class
> > for which solvers exist. The combinatorial nature still remains though
> > and only a local opitmum can be guaranteed unfortunately.
>
> > About your second question, you are right, I mistakenly gave an over
> > simplified specification of my problem. In fact, the inner problem
> > involves x_i's, but x_i's are treated as constants there and
> > optimization happens only with respect to a_k's. Although I gave a
> > wrong specification, your idea was general enough to capture that and
> > so we are on the right track. Your hints about optimality conditions
> > of the inner problem and the issue of complementarity were very
> > helpful.
>
> > Thanks!
>
> > G.D.
>
> > On Feb 26, 9:43 pm, Paul Rubin wrote:
> >> Bob Daniel kindly reminded me that complementarity constraints are a
> >> form of SOS1 constraint. =A0So a solver that handles SOS1 can be used,
> >> although that's still going to turn it into a partial enumeration
> >> problem (and raises some questions in my mind about how the bounding
> >> will be done).
>
> >> It occurs to me that I may have missed something obvious. =A0Going back=
to
> >> your original question, why not just solve the inner problem (to get th=
e
> >> a_k), then treat them as parameters (freezing the values) and solve the=

> >> outer problem to get the x_i?
>
> >> /Paul- Hide quoted text -
>
> >> - Show quoted text -
>
> how big is your problem?- Hide quoted text -
>
> - Show quoted text -