Optimality conditions for discrete optimal control problems

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

“…The obtained results are based on the general theory developed in [1] and they generalize our recent results obtained in [4] to the case of discrete optimal control problems with equality and inequality type of constraints on control and on endpoints.…”

“…Let (ξ,ŵ) be the optimal solution for the problem (1)- (4). Then there exists Lagrange multiplier λ such that the assertions of theorem 2.1 hold, and for every (h, v) ∈ H 1 2 (ξ,ŵ), such that (11) holds, we have…”

“…, 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].…”

Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints

“…eralized their recent results obtained in [21] to derive necessary optimality conditions to the case of discrete optimal control problems with equality and inequality type of constraints on control and on endpoints. Recently, we [31] have derived second-order optimality conditions for a discrete optimal control problem with control constraints and initial conditions, which are described by the sets.…”