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...

The linear programming problem is usually solved through the use of one of two algorithms: either simplex, or an algorithm in the family of interior point methods. In this article two representative members of the family of interior point methods are introduced and studied. We discuss the design of these interior point methods on a high level, and compare them to both the simplex algorithm and ...

Linear Complementarity Problems (LC Ps) belong to the class of NP-complete problems. Therefore we cannot expect a polynomial time solution method for LC Ps without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomialtime) form, in polynomial time either give a solution...

There are several classes of interior point algorithms that solve linear programming problems in O(Vin L) iterations, but it is not known whether this bound is tight for any interior point algorithm. Among interior point algorithms, several potential reduction algorithms combine both theoretical (O(+/E L) iterations) and practical efficiency as they allow the flexibility of line searches in the...