Paper Info
Title
Superlinear Convergence of an Infeasible Predictor-Corrector Path-Following Interior Point Algorithm for a Semidefinite Linear Complementarity Problem Using the Helmberg-Kojima-Monteiro Direction
Abstract
An 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 [C.-K. Sim and G. Zhao, Math. Program. Ser. A, 110 (2007), pp. 475-499], these off-central paths are shown to be well-defined 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 sufficient condition using these off-central paths that guarantees superlinear convergence of a predictor-corrector path-following interior point algorithm for SDLCP using the Helmberg-Kojima-Monteiro (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.
Year
DOI
Venue
2011
10.1137/090779279
SIAM Journal on Optimization
Keywords
Field
DocType
sufficient condition,accumulation point,search direction,helmberg-kojima-monteiro direction,hkm direction,infeasible predictor-corrector path-following interior,direction field,interior point,interior point algorithm,off-central path,interior point method,semidefinite linear complementarity problem,point algorithm,superlinear convergence,linear complementarity problem
Complementarity (molecular biology),Mathematical optimization,Ordinary differential equation,Mathematical analysis,Algorithm,Linear complementarity problem,Interior point method,Iterated function,Predictor–corrector method,Ode,Monotone polygon,Mathematics
Journal
Volume
Issue
ISSN
21
1
1052-6234
Citations 
PageRank 
References 
1
0.39
30
Authors
1
Name
Order
Citations
PageRank
Chee-Khian Sim1235.43