A Warm-Start Approach for Large-Scale
Stochastic Linear Programs

Technical Report MS 2006-004

Marco Colombo, J. Gondzio and A. Grothey

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.

PDF MS06-004.pdf.
Written: August 29, 2006, revised May 4, 2007 and March 12, 2009.
Mathematical Programming 127 (2011) 371-397.

Related Software:
HOPDM Higher Order Primal Dual Method.
OOPS Object-Oriented Parallel Solver.