Geodesic
The method of feasible directions for mathematical programming problems with preconvex constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 255-263 
V. I. Zabotin; T. F. Minnibaev. The method of feasible directions for mathematical programming problems with preconvex constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 255-263. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The convergence of the method of feasible directions is proved for the case of the smooth objective function and a constraint in the form of the difference of convex sets (the so-called preconvex set). It is shown that the method converges to the set of stationary points, which generally is narrower than the corresponding set in the case of a smooth function and smooth constraints. The scheme of the proof is similar to that proposed earlier by Karmanov.

[1] Zabotin V. I., Polonskii Yu. A., “Predvypuklye mnozhestva, otobrazheniya i ikh prilozheniya k ekstremalnym zadacham”, Kibernetika, 1981, no. 5, 71–74 | MR | Zbl

[2] Karmanov V. G., Matematicheskoe programmirovanie, Fizmatlit, M., 2004

[3] Zabotin V. I., Chernyaev Yu. A., “Obobschenie metoda proektsii gradienta na ekstremalnye zadachi s predvypuklymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 41:3 (2001), 367–373 | MR | Zbl