Asymptotic behavior of underlying NT paths in interior point methods for monotone semidefinite linear complementarity problems

2010-2011 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Underlying paths and local convergence behaviour of path-following interior point algorithm for SDLCP and SOCP

Ph.DDOCTOR OF PHILOSOPH

Asymptotic Behavior of HKM Paths in Interior Point Method for Monotone Semidefinite Linear Complementarity Problem: General Theory

Abstract An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field which in turn defines a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the systems of ODEs. In Then we show that if the given SDLCP has a unique solution, the first derivative of its off-central path, as a function of √ µ, is bounded. We work under the assumption that the given SDLCP satisfies strict complementarity condition