A global-filtering algorithm for linear programming problems with stochastic elements

In this paper, an interior-point based global filtering algorithm is proposed to solve linear programming problems with the right-hand-side and cost vectors being stochastic. Previous results on the limiting properties of the Kalman filtering process have been extended to handle some non-stationary situations. A global Kalman filter, across all iterations of the interior-point method, is designed to filter out noises while improving the objective value and reducing the primal and dual infeasibilities. Under appropriate assumptions, the proposed algorithm is shown to be globally convergent to an optimal solution of the underlying ‘true value’ system.