Dual regularization and Pontryagin's maximum principle in a problem of optimal boundary control for a parabolic equation with nondifferentiable functionals

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.