Primal-dual interior-point algorithm for linearly constrained convex optimization based on a parametric algebraic transformation

Abstract

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.