The authors present a primal-dual path following algorithm for solving linear and convex quadratic programming problems based on the logarithmic barrier function approach [

*A. V. Fiacco* and

*G. P. McCormick*, “Nonlinear programming: sequential unconstrained minimization techniques” (1968;

Zbl 0193.188)]. The present algorithm uses power series approximation of the path of solutions for the weighted barrier function family of problems associated with the given programming problem. They study the convergence properties of the algorithm and show that the complexity of the number of iterations depends on the order of approximation, say r. They also discuss the particular cases when

$r=1$ and

$r\to \infty $ and compare the convergence properties of the algorithm in these particular cases with those of some known polynomial-time primal-dual path following algorithms. No computational results for the algorithm are given.