Geodesic
On regularization of classical optimality conditions in convex optimal control
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 120-143

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We discuss regularization of two classical optimality conditions—the Lagrange principle (PL) and the Pontryagin maximum principle (PMP)—in a convex optimal control problem for a parabolic equation with an operator equality constraint and distributed initial and boundary controls. The regularized Lagrange principle and the Pontryagin maximum principle are based on two regularization parameters. These regularized principles are formulated as existence theorems for the original problem of minimizing approximate solutions.
Keywords: convex optimal control, operator constraint, boundary control, minimizing sequence, regularizing algorithm, Lagrange principle, Pontryagin maximum principle, dual regularization.
Mots-clés : parabolic equation 
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     author = {M. I. Sumin},
     title = {On regularization of classical optimality conditions in convex optimal control},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {120--143},
     publisher = {mathdoc},
     volume = {207},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_207_a12/}
}
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M. I. Sumin. On regularization of classical optimality conditions in convex optimal control. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 120-143. http://geodesic.mathdoc.fr/item/INTO_2022_207_a12/