A New Discrete Analogue of Pontryagin’s Maximum Principle

M. J. Mardanov^a^,^b^,*^,** and T. K. Melikov^a^,^c^,***
Translated by I. Ruzanova

^aInstitute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, AZ1141 Azerbaijan

^b Baku State University, Baku, AZ1148 Azerbaijan

^c Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku, AZ1141 Azerbaijan

Correspondence to: *e-mail: misir.mardanov@imm.az
Correspondence to: **e-mail: misirmardanov@yahoo.com
Correspondence to: ***e-mail: t.melik@rambler.ru

Received 26 June, 2018

Abstract—By introducing the concept of a γ-convex set, a new discrete analogue of Pontryagin’s maximum principle is obtained. By generalizing the concept of the relative interior of a set, an equality-type optimality condition is proved, which is called by the authors the Pontryagin equation.

DOI: 10.1134/S1064562418070049