The paper “First- and second-order necessary conditions with respect to components for discrete optimal control problems” of director of IMM ANAS, corr. member of ANAS, prof. M.Mardanov and senior research ass. of “Optimal Control” department, doctor of physico-mathematical sciences, prof. Telman Melikov was published in authoritative journal of Elsevir “Journal of Computational and Applied Mathematics” (Volume 364, 15 January 2020, 112342) indexed in the “Web of Sciences” base and implicated in Q₁ quartiles.

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is proved in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are proved.

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