Geodesic
Local search in problems with nonconvex constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 397-413

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Nonconvex optimization problems with an inequality constraint given by the difference of two convex functions (by a d.c. function) are considered. Two methods for finding local solutions to this problem are proposed that combine the solution of partially linearized problems and descent to a level surface of the d.c. function. The convergence of the methods is analyzed, and stopping criterions are proposed. The methods are compared by testing them in a numerical experiment. 
@article{ZVMMF_2007_47_3_a3,
     author = {T. V. Gruzdeva and A. S. Strekalovskii},
     title = {Local search in problems with nonconvex constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {397--413},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a3/}
}
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T. V. Gruzdeva; A. S. Strekalovskii. Local search in problems with nonconvex constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 397-413. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a3/