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

Abstract

We present a new way to view the off-central path in path-following interior point method for monotone semidefinite linear complementarity problem (SDLCP) and second order cone programming (SOCP). Using this definition, we show the existence of off-central path for SDLCP for general direction. Restricting to a particular direction, we analyse a simple SDP example to show that not all off-central paths are analytic at the optimal solution. We then investigate its implication on the local convergence behaviour of first-order predictor-corrector algorithm. We also give a necessary and sufficient condition for off-central path for general SDLCP to be analytic at the limit point when \mu = 0. Next, we show the existence of off-central path for SOCP for a particular direction. We then investigate asymptotic properties, for example, strict complementarity convergence, asymptotic analyticity, of these off-central paths.