Roos proved that the devised full-step infeasible algorithm has O(n) worst-case iteration complexity. This complexity bound depends linearly on a parameter ¯ κ(ζ), which is proved to be less than √ 2n. Based on extensive computational evidence (hundreds of thousands of randomly generated problems), Roos conjectured that ¯ κ(ζ) = 1 (Conjecture 5.1 in the above-mentioned paper), which would yield...

In this paper, we first present a brief infeasible interior-point method with full-Newton step for solving linear complementarity problem (LCP). The main iteration consists of a feasibility step and several centrality steps. First we present a full Newton step infeasible interior-point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introd...

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branch-and-bound algorithm in the outer iterations and an infeasible interior-point method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strate...

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is effective for problems containing both...

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

We present the convergence analysis of the inexact infeasible pathfollowing (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 to study the ...