Geodesic
Minimizing sequences in problems with d.c. constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 435-447

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Nonconvex optimization problems with a single inequality constraint given by the difference of two convex functions (i.e., by a d.c. function) are considered. Such problems may have many local solutions and stationary points that are far (in terms of, say, the value of the objective function) from a global solution. Necessary and sufficient conditions are proved for minimizing sequences in these problems. A global search strategy is proposed that is based on these conditions and uses classical methods of optimization. Its global convergence is proved. 
@article{ZVMMF_2005_45_3_a8,
     author = {A. S. Strekalovskii},
     title = {Minimizing sequences in problems with d.c. constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {435--447},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a8/}
}
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A. S. Strekalovskii. Minimizing sequences in problems with d.c. constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 435-447. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a8/