Related papers: On Lipschitz continuity of value functions for inf…
In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
This paper concerns a class of infinite horizon optimal control problems with state constraints. By extending the needle variation method to the infinite horizon case we obtain a complete set of necessary optimality conditions for a strong…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. Firstly, we provide an upper estimate of its Dini--Hadamard subdifferential in terms of the Clarke subdifferential of the…
We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional…
In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between…
This paper investigates the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. %with free right endpoint. In the papers of S.M.Aseev, A.V.Kryazhimskii, V.M.Veliov, K.O.Besov…
We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by $L^1$-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic…
This paper investigates the necessary conditions of optimality for uni- formly overtaking optimal control on infinite horizon with free right endpoint. Clarke's form of the Pontryagin Maximum Principle is proved without the as- sumption on…
In this paper we summarize our results in infinite horizon optimal control. We present optimality conditions for weak local minimizer in the framework of weighted functions. Moreover we formulate the Pontryagin Maximum Principle for strong…
New form of sufficient optimality condition is obtained in comparison with the Mangasarian sufficiency theorem. Both finite and infinite values of objective functional are allowed since concepts of overtaking and weakly overtaking…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
Necessary conditions of optimality in the form of the Pontryagin Maximum Principle are derived for the Bolza-type discounted problem with free right end. The optimality is understood in the sense of the uniformly overtaking optimality. Such…
The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…
We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…
In this work the synthesis of approximate optimal and smooth feedback laws for infinite horizon optimal control problems is addressed. In this regards, $L^{p}$ type error bounds of the approximating smooth feedback laws are derived,…
We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the the weakly overtaking criterion and the overtaking criterion, necessary boundary conditions on co-state arcs are deduced, these…