Geodesic
The use of local coordinates in optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 144-147

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The necessary and sufficient conditions for an extremum are expressed in local coordinates. It is shown that in some cases irregularity of the constraints at the extremum points does not affect the form of the necessary conditions. A first-order numerical method with a linear rate of convergence is considered. 
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     author = {D. V. Denisov},
     title = {The use of local coordinates in optimization problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {144--147},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a12/}
}
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D. V. Denisov. The use of local coordinates in optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 144-147. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a12/