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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022 Volume 207, Pages 120–143 (Mi into986)

This article is cited in 1 paper

On regularization of classical optimality conditions in convex optimal control

M. I. Suminab

a Tambov State University named after G.R. Derzhavin
b National Research Lobachevsky State University of Nizhny Novgorod

Abstract: 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, parabolic equation, operator constraint, boundary control, minimizing sequence, regularizing algorithm, Lagrange principle, Pontryagin maximum principle, dual regularization.

UDC: 517.9

MSC: 49K20, 49N15, 47A52

DOI: 10.36535/0233-6723-2022-207-120-143



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