This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). We introduce a kernel function in the algorithm. For p ∈ [0, 1), the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(n log n/ε).

The convergence of the Tapia indicators for infeasible{interior{point methods for solving degenerate linear complementarity problems is investigated. A new estimate of the rate of convergence of the Tapia indicators for the indices where both primal and dual variables vanish in the solution is obtained, showing that Tapia indicators for these indices converge slower than for other indices. Use ...

In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obt...

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110– 1136, 2006). We introduce a special self-regular proximity to induce the feasibility step and to verify quadratic convergence. The result of polynomial complexity coincides with the best-known iteration bound for infeasib...

We establish polynomial-time convergence of infeasible-interior-point methods for conic programs over symmetric cones using a wide neighborhood of the central path. The convergence is shown for a commutative family of search directions used in Schmieta and Alizadeh [9]. These conic programs include linear and semidefinite programs. This extends the work of Rangarajan and Todd [8], which establi...

Linear complementarity problem noted (LCP) becames in present the subject of many reseach interest because it arises in many areas and it includes the two important domains in optimization:the linear programming (LP) and the convex quadratic (CQP) programming. So the researchers aims to extend the results obtained in (LP) and (CQP) to (LCP). Differents classes of methods are proposed to solve (...

In [4] the second author presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(n...