Geodesic
Necessary optimality conditions in non-smooth problems with equality constraints
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 72-83

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Necessary conditions for extremum in non smooth problems are obtained in this article. The problem under consideration includes both equality and inequality type constrains given by non-smooth functions. The necessary conditions are given in terms of asymptotic subdifferentials. Generalized Lagranges's multiplier rule for non-smooth problems with not local lipschitz constraints is obtained. It is proved also that Peno's and Clark's generalized derivatives are upper convex approximations for local Lipshitz functions. 
@article{VMJ_2016_18_3_a7,
     author = {R. A. Khachatryan},
     title = {Necessary optimality conditions in non-smooth problems with equality constraints},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {72--83},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a7/}
}
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R. A. Khachatryan. Necessary optimality conditions in non-smooth problems with equality constraints. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 72-83. http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a7/