Marco Colombo, J. Gondzio and A. Grothey
Abstract
We describe a method of generating a warm-start point for
interior point methods in the context of stochastic programming.
Our approach exploits the structural information of the stochastic
problem so that it can be seen as a structure-exploiting initial
point generator. We solve a small-scale version of the problem
corresponding to a reduced event tree and use the solution to generate
an advanced starting point for the complete problem. The way we
produce a reduced tree tries to capture the important information in
the scenario space while keeping the dimension of the corresponding
(reduced) deterministic equivalent small. We derive conditions
which should be satisfied by the reduced tree to guarantee a successful
warm-start of the complete problem. The implementation within
the HOPDM and OOPS interior point solvers shows remarkable advantages.
Key words: Warm-Start, Interior Point Methods, Stochastic Programming.