Second-order optimality conditions in a discrete optimal control problem

Optimality conditions for discrete optimal control problems with equality and inequality type of constraints

“…(3). Also, it can be considered the initial problem with equality and inequality type of state constraints.…”

“…, x N ). If the conditions (2), (3) and (4) are satisfied then we say that the pair (x 0 , w) is feasible. The discrete optimization problem is to minimize the function…”

“…From numerous literature we refer, for example, to [6,7,4]. Note that some results about first and second-order necessary optimality conditions for discrete optimal control problems without normality assumptions can be found in [2,3]. Also,we refer to [5] where there are many results about discrete optimization problems.…”

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

“…It is well known that the optimal control problems with continuous variables can be transferred to discrete optimal control problems by discretization. During the past decades, several papers dealing with the first‐order optimality condition and the second‐order necessary condition for discrete optimal control have appeared in the literature; see, for example, References 9‐16 and the references therein. Under the assumption that the cost functions are convex with respect to control variables, Ioffe and Tikhomirov 14 (theorem 1 of sect.…”

Optimality conditions for discrete calculus of variations problems

“…Note that some results about first-and second-order necessary optimality conditions in discrete optimal control problems without normality assumptions can be found in [2,6]. Also, we refer to [7,8] where there are first-order optimality conditions for general discrete optimal control problems and for the problems arising from discrete approximations.…”