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Chee Khian Sim(macksiminet.polyu.edu.hk) Abstract: Interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [31], these offcentral paths are shown to be welldefined analytic curves and any of their accumulation points is a solution to a given monotone semidefinite linear complementarity problem (SDLCP). The study of these paths provides a way to understand how iterates generated by an interior point algorithm behave. In this paper, we give a weak sufficient condition using these offcentral paths that guarantees superlinear convergence of a predictorcorrector pathfollowing interior point algorithm for SDLCP using the HKM direction. This sufficient condition is implied by a currently known sufficient condition for superlinear convergence. Using this sufficient condition, we show that for any linear semidefinite feasibility problem, superlinear convergence using the interior point algorithm, with the HKM direction, can be achieved, for a suitable starting point. We work under the assumption of strict complementarity. Keywords: Semidefinite linear complementarity problem; Linear semidefinite feasibility problem Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Submitted. Download: [PDF] Entry Submitted: 01/24/2010 Modify/Update this entry  
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