Geodesic
Dual regularization and Pontryagin's maximum principle in a~problem of optimal boundary control for a~parabolic equation with nondifferentiable functionals
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 229-244

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A problem of optimal boundary control is considered for a`divergent linear parabolic equation. Equality constraints of the problem are given by nondifferentiable functionals. A dual regularization algorithm stable to errors in initial data is constructed for solving the problem. Pontryagins maximum principle plays the key role in this algorithm.
Keywords: duality, regularization, optimal boundary control, nondifferentiable functional, maximum principle. 
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     author = {M. I. Sumin},
     title = {Dual regularization and {Pontryagin's} maximum principle in a~problem of optimal boundary control for a~parabolic equation with nondifferentiable functionals},
     journal = {Trudy Instituta matematiki i mehaniki},
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M. I. Sumin. Dual regularization and Pontryagin's maximum principle in a~problem of optimal boundary control for a~parabolic equation with nondifferentiable functionals. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 229-244. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a18/