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

Abstract

We consider nonlinear discrete optimal control problems with variable endpoints and with equality and inequality type of constraints on control. We derive new nontrivial first and second-order necessary optimality conditions. Mathematics Subject Classification (2000). 49K99, 93C55, 90C46.

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.…”

“…6.4) established the first‐order necessary optimality conditions for discrete optimal control problems with control constraints which are described by the sets. By using the 2‐regularity condition 8 and applying necessary optimality conditions for a mathematical programming problem, Marinkovíc 12 generalized his/her recent results obtained in Reference 11 to derive necessary optimality conditions for discrete optimal control problems with equality and inequality type of constraints on control and on endpoints. Recently, we 15,16 have derived second‐order optimality conditions for a discrete optimal control problem with a nonconvex cost function, linear state equations, and mixed constraints.…”

Optimality Conditions for Discrete Optimal Control Problems

“…Recently, the study of sufficient optimality conditions of the optimal control problems has received much attention from many authors (see for example [1,2] and the references therein). In the same time, the study of the optimality conditions of discrete optimal control problems is also of interest to many researchers (see, for example [3][4][5][6][7][8], and the references therein).…”

Problemas de controle ótimo discreto com restrições mistas

“…Em 2008, Marinkovíc obteve condições necessárias de otimalidade necessárias de primeira e segunda ordem para problemas de controle ótimo discreto com restrições de igualdade e desigualdade no controle e nas restrições de contorno (ver [18]), este resultado foi generalizado em [19]. Em 2015, Toan, Ansari e Yao obtiveram condições necessárias de segunda ordem para problemas COD com função objetivo não convexa e restrições de controle abstratas (ver [20]).…”