Second‐order necessary optimality conditions for a discrete optimal control problem with nonlinear state equations

Abstract

Summary In this article, we study second‐order necessary optimality conditions for a discrete optimal control problem with a nonconvex cost function, nonlinear state equations and mixed constraints. In order to achieve these conditions, we first establish an abstract result on the second‐order necessary optimality conditions for a mathematical programming problem and then we derive the second‐order necessary optimality conditions for a discrete optimal control problem. The main result of this article is illustrated by two examples.