Geodesic
Necessary Conditions for an Extremum in a Mathematical Programming Problem
Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 6-30

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For minimization problems with equality and inequality constraints, first- and second-order necessary conditions for a local extremum are presented. These conditions apply when the constraints do not satisfy the traditional regularity assumptions. The approach is based on the concept of 2-regularity; it unites and generalizes the authors' previous studies based on this concept. 
@article{TRSPY_2007_256_a0,
     author = {E. R. Avakov and A. V. Arutyunov and A. F. Izmailov},
     title = {Necessary {Conditions} for an {Extremum} in a {Mathematical} {Programming} {Problem}},
     journal = {Informatics and Automation},
     pages = {6--30},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a0/}
}
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E. R. Avakov; A. V. Arutyunov; A. F. Izmailov. Necessary Conditions for an Extremum in a Mathematical Programming Problem. Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 6-30. http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a0/