Geodesic
Stable sequential Pontryagin maximum principle in optimal control problems with phase restrictions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 102-113

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In this paper, we obtain optimality conditions in an optimal control problem with pointwise phase constraints of the equality and inequality types treated as constraints in a Hilbert space. The main results of this work are the regularized, stable under errors of source data, Lagrange principle and the pointwise Pontryagin maximum principle in the iterative form, which, in turn, yield a functional way of constructing a minimizing approximate solution to the problem considered.
Keywords: optimal control, ill-posed problem, dual regularization, iterative dual regularization. 
@article{INTO_2019_171_a8,
     author = {F. A. Kuterin and A. A. Evtushenko},
     title = {Stable sequential {Pontryagin} maximum principle in optimal control problems with phase restrictions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {102--113},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a8/}
}
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F. A. Kuterin; A. A. Evtushenko. Stable sequential Pontryagin maximum principle in optimal control problems with phase restrictions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 102-113. http://geodesic.mathdoc.fr/item/INTO_2019_171_a8/