This article is cited in 4 papers

On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems

Anton O. Belyakov<sup>abcd

a</sup> Moscow School of Economics, Lomonosov Moscow State University, Leninskie Gory 1, str. 61, Moscow, 119234 Russia
^b National Research Nuclear University “MEPhI,” Kashirskoe sh. 31, Moscow, 115409 Russia
^c National University of Science and Technology “MISiS,” Leninskii pr. 4, Moscow, 119049 Russia
^d Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418 Russia

Abstract: We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control.

UDC: 517.977.52

Received: September 27, 2019
Revised: January 21, 2020
Accepted: February 25, 2020

DOI: 10.4213/tm4092

 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 308, 56–66

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