A weighted logarithmic barrier interior-point method for linearly constrained optimization

Abstract

In this paper, a weighted logarithmic barrier interior-point method for linearly convex constrained optimization problems is presented. The proposed method is based on the weighted-path where instead of a scalar barrier parameter used in the classical path methods, a weighted positive vector is associated with the perturbed barrier problems. This modification gives a theoretical flexibility on its convergence and its numerical performance. In addition, this method is of Newton descent direction and the computation of the step-size along this direction is based on a new efficient technique called the tangent method. The practical efficiency of our approach is shown by giving some numerical results.