A Weighted-path Following Interior-point Algorithm for Convex Quadratic Optimization Based on Modified Search Directions

Getting a perfectly centered initial point for feasible path-following interior-point algorithms is hard practical task. Therefore, it worth to analyze other cases when the starting not necessarily centered. In this paper, we propose short-step weighted-path following algorithm (IPA) solving convex quadratic optimization (CQO). The latter based on modified search direction which obtained by technique of algebraically equivalent transformation (AET) introduced new univariate function Newton system defines weighted-path. At each iteration, uses only full-Newton steps and strategy central-path tracing approximately We show that well-defined converges locally quadratically an optimal solution CQO. Moreover, obtain currently best known iteration bound, namely, $\mathcal{O}\left(\sqrt{n}\log \dfrac{n}{\epsilon}\right)$ as good bound linear analogue. Some numerical results are given evaluate efffficiency algorithm.