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

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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. 
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     author = {V. I. Zabotin and T. F. Minnibaev},
     title = {The method of feasible directions for mathematical programming problems with preconvex constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {255--263},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a6/}
}
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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/