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.
In this paper, we present a primal-dual interior-point algorithm for convex quadratic programming problem based on a new parametric kernel function with an hiperbolic–logarithmic barrier term. Using the proposed kernel function we show some basic properties that are essential to study the complexity analysis of the correspondent algorithm which we find it coincides with the best know iteration bounds for large-update method, namely, O (√ n log n log n/ε) by a special choice of the parameter p > 1.
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