1997 journal article

Linear programming with stochastic elements: An on-line approach

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 33(9), 61–82.

By: S. Guan n & S. Fang n

co-author countries: United States of America 🇺🇸
author keywords: linear programming; infeasible-interior-point method; stochastic programming; Kalman filter
Source: Web Of Science
Added: August 6, 2018

In this paper, we study linear programming problems with both the cost and right-hand-side vectors being stochastic. Kalman filtering techniques are integrated into the infeasible-interior-point method to develop an on-line algorithm. We first build a “noisy dynamic model” based on the Newton equation developed in the infeasible-interior-point method. Then, we use Kalman filtering techniques to filter out the noise for a stable direction of movement. Under appropriate assumptions, we show a new result of the limiting property of Kalman filtering in this model and prove that the proposed on-line approach is globally convergent to a “true value solution” in the mode of quadratic mean.