Article ID: | iaor20062914 |
Country: | Canada |
Volume: | 1 |
Issue: | 1 |
Start Page Number: | 3 |
End Page Number: | 19 |
Publication Date: | Jan 2006 |
Journal: | Algorithmic Operations Research |
Authors: | Murty Katta G. |
Keywords: | interior point methods |
In this paper we briefly review the importance of LP (linear programming), and Dantzig's main contributions to OR (Operations Research), mathematics, and computer science. In earlier papers gravitational methods for LP have been introduced. Several versions exist. The three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and (c): the ball of largest possible radius with the given center that will completely fit within the polytope, with the option of changing its radius as the algorithm progresses. In versions (a) and (b), after the first move, the center of the ball always remains very close to the boundary (because the ball hugs the boundary), and hence these versions behave like other boundary algorithms such as the simplex algorithm in terms of exponential complexity in the worst case. Here we discuss a gravitational method of type (c) that behaves like an interior point method. To guarantee that the ball has the largest possible radius, it uses a new centering strategy that moves any interior feasible solution