Abstract. The paper presents an overview of the studies stimulated by fundamental works of B.N. Pshenichnyi in the field of necessary conditions for extremum, numerical methods of optimization, theory of optimal control, and differential games. Among them are investigations related to new scientific fields such as processes with fractional derivatives and impulsive control systems. Refs: 102 titles.

Keywords: optimization, linearization method, directional derivative, multi-valued mappings, convex analysis, necessary extremum conditions, differential games, Dirac delta function, Minkowski functional, Auman integral, Pontryagin’s condition, Cauchy formula, Mitta-Leffler generalized matrix function, Riemann–Liouville fractional derivative.