sci.op-research

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=A0pm, 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 the
> 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 -