Geodesic
Study of a logarithmic barrier approach for linear semidefinite programming
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 300-312

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In this paper, we present a logarithmic barrier interior-point method for solving a semidefinite programming problem. Newton's method is used to compute the descent direction, and minorant function are used as an efficient alternative to line search methods to determine the displacement step along the direction in order to reduce the computation cost.
Keywords: semidefinite programming, interior-point methods, logarithmic barrier methods, line search. 
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Assma Leulmi; Bachir Merikhi; Djamel Benterki. Study of a logarithmic barrier approach for linear semidefinite programming. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 300-312. http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a4/