  In this paper, we present an interior point algorithm with a full-Newton step
for solving a linearly constrained convex optimization problem, in which we
propose a generalization of the work of Kheirfam and Nasrollahi
\cite{kheirfam2018full}, that consists in determining the descent directions
through a parametric algebraic transformation. The work concludes with a
complete study of the convergence of the algorithm and its complexity, where we
show that the obtained algorithm achieves a polynomial complexity bounds.
