Geodesic
Newton's method for the solution of systems of equalities and inequalities
Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 635-640.

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An algorithm is constructed generalizing Newton's method to apply to the solution of systems of nonlinear equations and inequalities. It is proved that the convergence of the algorithm is of the second order. 
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     author = {B. N. Pshenichnyi},
     title = {Newton's method for the solution of systems of equalities and inequalities},
     journal = {Matemati\v{c}eskie zametki},
     pages = {635--640},
     publisher = {mathdoc},
     volume = {8},
     number = {5},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a10/}
}
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B. N. Pshenichnyi. Newton's method for the solution of systems of equalities and inequalities. Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 635-640. http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a10/