Geodesic
The maximum principle residual functional in optimal control theory
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1133-1149

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The possibilities of applying results related to the so-called maximum principle residual functional to justify and design algorithms for solving optimal control problems and discussed. The differential properties of the value function of the optimal control problem are established. A dual method for solving the optimal control problem, based on maximizing the value function of a modified Lagrange functional, is described. 
@article{ZVMMF_1990_30_8_a1,
     author = {M. I. Sumin},
     title = {The maximum principle residual functional in optimal control theory},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1133--1149},
     publisher = {mathdoc},
     volume = {30},
     number = {8},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a1/}
}
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M. I. Sumin. The maximum principle residual functional in optimal control theory. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1133-1149. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a1/