Cartis, Coralia (2005) Some New Results Concerning the PrimalDual PathFollowing Interior Point Algorithm for Linear Programming. Technical Report. Unspecified. (Submitted)

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Abstract
The PrimalDual (PD) pathfollowing interior point algorithm for solving Linear Programming (LP) problems is considered. Firstly, we investigate its convergence and complexity properties when a new longstep linesearch procedure suggested by M. J. D.Powell is employed. Assuming that a primaldual strictly feasible starting point is available and that the centring parameters are bounded away from zero, we show that the duality gap of the iterates tends to zero, thereby proving that the limit points of the sequence of iterates are solutions of the problem. Further, we consider whether the limit points of the sequence of iterates generated by some longstep variants of the algorithm coincide with the analytic centre of the primaldual solution set of the problem. Because of the difficulty of the analysis involved, we restrict attention to the case when the standard form of the problem has one equality constraint and multiple solutions. We find that, when the centring parameters are bounded away from zero, the sequence of iterates does converge to the analytic centre. When the centring parameters tend to zero asymptotically at the same rate as the duality gap of the iterates, however, we show that in exact arithmetic the sequence of iterates may have other limit points in the solution set.
The author was supported through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the UK
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1147 
Deposited By:  Lotti Ekert 
Deposited On:  13 May 2011 07:19 
Last Modified:  29 May 2015 18:50 
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