Geodesic
Shooting method for solving equilibrium programming problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2008-2013

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A new iterative method is proposed for solving equilibrium programming problems. The sequence of points it generates is proved to converge weakly to the solution set of the equilibrium problem under study. If the initial point has at least one projection onto the solution set of the equilibrium problem, the sequence generated by the method is shown to converge strongly to the set of these projections. The partial gradient of the initial data is assumed to be invertible and strictly monotone, which differs from the classical skew-symmetry condition. 
@article{ZVMMF_2013_53_12_a5,
     author = {B. A. Budak},
     title = {Shooting method for solving equilibrium programming problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2008--2013},
     publisher = {mathdoc},
     volume = {53},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a5/}
}
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B. A. Budak. Shooting method for solving equilibrium programming problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2008-2013. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a5/