Cartis, Coralia (2005) On the Convergence of a PrimalDual Second0rder Corrector Interior Point Algorithm for Linear Programming. Technical Report. Unspecified. (Submitted)

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Abstract
The PrimalDual Second Order Corrector (PDSOC) algorithm that we investigate computes on each iteration a corrector direction in addition to the direction of the standard primaldual pathfollowing interior point method (Kojima et al, 1989) for Linear Programming (LP), in an attempt to improve performance. The corrector is multiplied by the square of the stepsize in the expression of the new iterate. While the outline of the PDSOC algorithm is known (Zhang et al, 1995), we present a substantive theoretical interpretation of its construction. Further, we investigate its convergence and complexity properties, provided that a primaldual strictly feasible starting point is available. Firstly, we use a new longstep linesearch technique suggested by M J D Powell, and show that, when the centring parameters are bounded away from zero, the limit points of the sequence of iterates are primaldual strictly complementary solutions of the LP problem. We consider also the popular choice of letting the centring parameters be of the same order as the duality gap of the iterates, asymptotically. A standard longstep linesearch is employed to prove that the sequence of iterates converges to a primaldual strictly complementary solution of the LP problem, which may not be the analytic centre of the primaldual solution set as further shown by an example.
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:  1149 
Deposited By:  Lotti Ekert 
Deposited On:  13 May 2011 07:18 
Last Modified:  29 May 2015 18:50 
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