Geodesic
A logarithmic barrier approach via majorant function for nonlinear programming
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 528-539

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In this paper, we are interested in solving an optimization nonlinear programming problem using a logarithmic barrier interior point method, in which the penalty term is taken as a vector $ r \in \mathbb{R}^{n}_{+} $. The descent direction has been calculated using a classical Newton method, however the step size has been calculated with a new technique of majorant functions and a secant technique. The numerical simulations show us the efficiency of our approach compared to the classical line search method.
Keywords: nonlinear convex programming, logarithmic penalty method, line search, majorant function
Mots-clés : secant technique. 
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     title = {A logarithmic barrier approach via majorant function for nonlinear programming},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2023},
     language = {en},
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Boutheina Fellahi; Bachir Merikhi. A logarithmic barrier approach via majorant function for nonlinear programming. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 528-539. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a10/