<p style='text-indent:20px;'>The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an as wCP may lead highly efficient algorithms for its numerical solution, is nontrivial generalization the problem. In this paper we consider special linear (wLCP), which more general optimization Fisher...

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...

‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programmin...

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...

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).

We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after m steps) for solving nonlinear equations, F(x) = 0, F : D ⊆ Rn → Rn. We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given n, there exist thresholds of m, that is an interval (...

We present an improved version of an infeasible interior-point method for linear optimization published in 2006. In the earlier version each iteration consisted of one so-called feasibility step and a few – at most three – centering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the earlier bound by a factor 2 √ 2. The improvements ...

In this paper we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problem (HLCP). This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by suitable perturbation in HLCP problem. Then, we use so-called feasibility steps that serves to generate strictly feasible iterates for the ...

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...

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).