Geodesic
Theoretical justification of interior point algorithms for solving optimization problems with nonlinear constraints
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 27-38.

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A family of interior point algorithms is considered. These algorithms can be used for solving mathematical programming problems with nonlinear inequality constraints. The weighted Euclidean rates are applied to find a descent direction for improving a solution. These rates are varying in iterations. Theoretical justification of the algorithms with some assumptions (such as non-degeneracy of a problem) is presented. 
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V. I. Zorkaltsev; S. M. Perzhabinsky. Theoretical justification of interior point algorithms for solving optimization problems with nonlinear constraints. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a2/

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