# On Hamiltonian as Limiting Gradient in Infinite Horizon Problem

@article{Khlopin2015OnHA, title={On Hamiltonian as Limiting Gradient in Infinite Horizon Problem}, author={D. Khlopin}, journal={Journal of Dynamical and Control Systems}, year={2015}, volume={23}, pages={71-88} }

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 process is assumed to exist, and the corresponding payoff of the optimal process (expressed in the form of improper integral) is assumed to converge in the Riemann sense. No other assumptions on the asymptotic behaviour of trajectories or adjoint variables…

## 3 Citations

Necessary Conditions In Infinite-Horizon Control Problem That Need No Asymptotic Assumptions.

- Mathematics
- 2019

We consider a Bolza-type infinite-horizon control problem with free right end. We propose a modification of Halkin's general construction of necessary conditions of optimality in which the…

Necessary conditions in terms of value functions for infinite horizon problem

- Mathematics
- 2015

We investigate conditions of optimality for the infinite horizon control problem and consider their correspondence with the value function. In particular, the sensitivity relations hold if the value…

On Lipschitz continuity of value functions for infinite horizon problem

- Mathematics
- 2015

We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we…

## References

SHOWING 1-10 OF 35 REFERENCES

Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems

- Mathematics
- 2012

This paper refines the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. This condition is applicable to general non-stationary…

Necessary conditions in terms of value functions for infinite horizon problem

- Mathematics
- 2015

We investigate conditions of optimality for the infinite horizon control problem and consider their correspondence with the value function. In particular, the sensitivity relations hold if the value…

Value Functions and Transversality Conditions for Infinite Horizon Optimal Control Problems

- Mathematics, Computer ScienceMCO
- 2008

The sufficiency theorem presented in this paper employs the strengthened adjoint inclusion of the value function as well as the strengthened maximum principle, which indicates the relationship between the maximum principle and dynamic programming.

On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems

- Mathematics
- 2014

For a class of infinite-horizon optimal control problems that appear in studies on economic growth processes, the properties of the adjoint variable in the relations of the Pontryagin maximum…

Necessity of limiting co-state arcs in Bolza-type infinite horizon problem

- Mathematics
- 2015

We investigate necessary conditions of optimality for the Bolza-type infinite horizon problem with free right end. The optimality is understood in the sense of weakly uniformly overtaking optimal…

The Pontryagin maximum principle and optimal economic growth problems

- Mathematics
- 2007

This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes.…

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

- Computer Science, MathematicsIEEE Conference on Decision and Control and European Control Conference
- 2011

The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity, which improves on the currently available necessary conditions of optimality for infinite horizon problems.

Transversality condition for infinite-horizon problems

- Mathematics
- 1996

We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of…

On the value function for nonautonomous optimal control problems with infinite horizon

- Computer Science, MathematicsSyst. Control. Lett.
- 2007

The equivalence between dynamic programming inequalities and Hamilton–Jacobi–Bellman (HJB) inequalities for proximal sub (super) gradients is proven and it is shown that the value function is a Dini solution of the HJB equation.

Conditions implying the vanishing of the Hamiltonian at infinity in optimal control problems

- Mathematics, Computer ScienceOptim. Lett.
- 2009

In an infinite horizon optimal control problem the Hamiltonian vanishes at infinity when the differential equation is autonomous and the integrand in the criterion satisfies some weak integrability…