Efficient inverse barrier method for nonlinear optimization

Aicha Kraria^a, Bachir Merikhi^a, Djamel Benterki^a, Adnan Yassine<sup>b

a</sup> Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Setif 1 University Ferhat Abbas, Setif, 19000, Algeria
^b Laboratory of Applied Mathematics of Le Havre, Le Havre University Normandy, 76600, Le Havre, France

Abstract: In this paper, we use a new variant of inverse barrier method to solve a nonlinear optimization problem. The new inverse barrier function depends on the components of the penalty vector and preserves the properties of the original problem. The descent direction is calculated using Newton's method, while the step size is calculated using the tangent technique and the backtracking with interpolation technique in parallel with Wolfe's method.
Comparative numerical simulations are presented as a support for our approach.

Keywords: interior point method, nonlinear programming, inverse barrier method.

UDC: 517.8

Received: 28.03.2025
Received in revised form: 21.08.2025
Accepted: 27.09.2025

Language: English