In this paper we present the convergence analysis of the inexact infeasible path-following (IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary...

Abstract In this paper, we suggest a new infeasible interior-point method (IIPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -linear complementarity problem ( -LCP) based on class of kernel func...

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...

We present a full-Newton step infeasible interior-point algorithm. It is shown that at most O(n) (inner) iterations suffice to reduce the duality gap and the residuals by the factor 1 e . The bound coincides with the best known bound for infeasible interior-point algorithms. It is conjectured that further investigation will improve the above bound to O( √ n).

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasibl...

This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd step for semidefinite programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). The polynomial bound coincides with that of infeasible interior-point methods for linear programming, namely, O(n log n/ε).