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

TL;DR

An interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which a generalization of the work of Kheirfam and Nasrollahi that consists in determining the descent directions through a parametric algebraic transformation is proposed.

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.

Theorems & Definitions (16)

• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• Lemma 4
• proof
• Lemma 5
• proof