Geodesic
On the application of Newton-type methods to Fritz John optimality conditions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1194-1208

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An approach to the numerical solution of optimization problems with equality constraints violating the traditional constraint qualification is developed. According to this approach, an (overdetermined) defining system is constructed based on the Fritz John optimality conditions and the Gauss–Newton method is applied to this system. The assumptions required for the implementability and local superlinear convergence of the resulting algorithm are completely characterized in terms of the original problem. 
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     author = {A. F. Izmailov and E. I. Uskov},
     title = {On the application of {Newton-type} methods to {Fritz} {John} optimality conditions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1194--1208},
     publisher = {mathdoc},
     volume = {51},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a2/}
}
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A. F. Izmailov; E. I. Uskov. On the application of Newton-type methods to Fritz John optimality conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1194-1208. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a2/