Geodesic
Linear optimal control problem with convex homogeneous functional
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 757-763.

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The iterative method of solving the linear optimal control problem with convex homogeneous nonnegative functional is proposed. As the approach based on the Pontryagin maximum principle, this one is characterized by using supporting properties of convex sets and approximations of convex sets with a family of adjacent simplices. 
@article{FPM_1999_5_3_a6,
     author = {G. V. Shevchenko},
     title = {Linear optimal control problem with convex homogeneous functional},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {757--763},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a6/}
}
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G. V. Shevchenko. Linear optimal control problem with convex homogeneous functional. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 757-763. http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a6/