A Newton descent logarithmic barrier interior-point algorithm for monotone LCP

¹ Laboratory of Fundamental and Numerical Mathematics, University Ferhat Abbas Sétif 1, Sétif 19000, Algeria
² Normandie University, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76700 Le Havre, France

^* Corresponding author: welid.gimes@univ-setif.dz

Received: 9 November 2023
Accepted: 20 November 2024

Abstract

The growing importance of the monotone linear complementarity problems (LCP) lies in the different applications it covers, both in mathematics and in practice. In this paper, based on the optimization techniques, we propose a descent logarithmic barrier interior-point method for solving the (LCP). The idea is to transform the LCP into an equivalent convex quadratic optimization problem, denoted by (CQO). Then, the associated barrier problem to CQO is formulated. The existence and the uniqueness of optimal solution of the barrier problem is showed. For its numerical aspects, the descent direction is computed by using the classical Newton’s method. However, to determine the displacement step along this direction, guaranteeing the maintenance of the new iterates inside the domain during the algorithm process and the improvement of the value of the objective function, we apply a new approach using approximation functions known as “minorant and majorant approximating functions”. The numerical results obtained are very promising and show the effectiveness of this new strategy.