This paper presents a path-following full-Newton step interior-point algorithm for solving monotone linear complementarity problems. Under new choices of the defaults of the updating barrier parameter [Formula: see text] and the threshold [Formula: see text] which defines the size of the neighborhood of the central-path, we show that the short-step algorithm has the best-known polynomial complexity, namely, [Formula: see text]. Finally, some numerical results are reported to show the efficiency of our algorithm.
In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.
Abstract
We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from the implementation point of view. We studied two variants, which differ only in the method of updating the parameter which characterizes the central path. The implementation was done in the C++ programming language and the obtained numerical results prove the efficiency of the proposed method.
A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem
