A Parallel Interior Point Method for Stochastic Linear Programs

This paper describes a parallel implementation of the primal-dual interior point method for a special class of large linear programs that occur in stochastic linear programming. The method used by Vanderbei and Carpenter [31] for removing dense columns is modi ed to eliminate variables which link blocks in stochastic linear programs. The algorithm developed was tested on six test problems from the Ho and Loute's collection of staircase linear programs [14] and on nine multi-scenario stochastic network problems [27] which arise in portfolio management. Numerical results demonstrate the e ciency of the resulting algorithm. For an 800 scenario problem with 91 constraints and 248 variables per scenario, a parallel e ciency of 99% is achieved.