Geodesic
The Lagrange principle and the Pontryagin maximum principle in ill-posed optimal control problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 63-78

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We consider the regularization of the classical optimality conditions—the Lagrange principle and the Pontryagin maximum principle—in a convex optimal control problem for a parabolic equation with distributed and boundary controls, and also with a finite number functional equality constraints given by ‘`point’ functionals nondifferentiable in the Fréchet sense, which are the values of the solution of the third initial-boundary-value problem for the specified equation at preselected fixed (possibly boundary) points of the cylindrical domain of the independent variables.
Keywords: convex optimal control, boundary control, Fréchet nondifferentiable functional, Steklov averaging, minimizing sequence, dual regularization, regularizing algorithm, Lagrange principle, Pontryagin maximum principle.
Mots-clés : parabolic equation 
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     title = {The {Lagrange} principle and the {Pontryagin} maximum principle in ill-posed optimal control problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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M. I. Sumin. The Lagrange principle and the Pontryagin maximum principle in ill-posed optimal control problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 63-78. http://geodesic.mathdoc.fr/item/INTO_2022_208_a7/