Sufficient Conditions in Optimal Control Theory

Seierstad, Atle; Sydsæter, Knut

doi:10.2307/2525753

Cited by 285 publications

(155 citation statements)

References 11 publications

Supporting

Mentioning

133

Contrasting

Unclassified

Order By: Relevance

“…by optimizing the current value of the Hamiltonian (Pinch, 1993;Seierstad and Sydsaeter, 1986) for the disease dynamics equations subject to the constraints of the epidemiological and economic system. Here, we denote respectively by p 1 and p 2 the intrinsic value attached to a healthy individual of species 1 and 2: r is the discount rate.…”

Section: Optimal Controlmentioning

confidence: 99%

See 1 more Smart Citation

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Ndeffo-Mbah¹,

Gilligan²

2010

Journal of Theoretical Biology

View full text Add to dashboard Cite

There is growing interest in incorporating economic factors into epidemiological models in order to identify optimal strategies for disease control when resources are limited. In this paper we consider how to optimize the control of a pathogen that is capable of infecting multiple hosts with different rates of transmission within and between species. Our objective is to find control strategies that maximize the discounted number of healthy individuals. We consider two classes of host-pathogen system, comprising two host species and a common pathogen, one with asymmetrical and the other with symmetrical transmission rates, applicable to a wide range of SI (susceptible-infected) epidemics of plant and animal pathogens. We motivate the analyses with an example of sudden oak death in California coastal forests, caused by Phytophthora ramorum, in communities dominated by bay laurel (Umbellularia californica) and tanoak (Lithocarpus densiflorus). We show for the asymmetric case that it is optimal to give priority in treating disease to the more infectious species, and to treat the other species only when there are resources left over. For the symmetric case, we show that although a switching strategy is an optimum, in which preference is first given to the species with the lower level of susceptibles and then to the species with the higher level of susceptibles, a simpler strategy that favours treatment of infected hosts for the more susceptible species is a robust alternative for practical application when the optimal switching time is unknown. Finally, since transmission rates are notoriously difficult to estimate, we analyze the robustness of the strategies when the true state with respect to symmetry or otherwise is unknown but one or other is assumed.

show abstract

Section: Optimal Controlmentioning

confidence: 99%

“…f 2 (and hence f 1 ) has to be chosen so as to maximize the Hamiltonian (Seierstad and Sydsaeter, 1986). Maximization yields the following result:…”

Section: First Case: α Satisfies Eqmentioning

confidence: 99%

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Ndeffo-Mbah¹,

Gilligan²

2010

Journal of Theoretical Biology

View full text Add to dashboard Cite

show abstract

“…Assumptions (C1)-(C5) imply that the sufficient condition in [11] can be applied. This is the main idea of the proof.…”

Section: Proposition 21mentioning

confidence: 99%

“…This fact and the uniqueness of solution imply that the solutionˆ ( ) corresponding toˆ 1 andˆ 2 , and starting from 0 > 0 remains positive on the time interval, where it is defined. According to the sufficient optimality conditions for the optimal control problem (8)-(11) (see [11]), the relations 1 :…”

Section: Proposition 21mentioning

confidence: 99%

Feedback Nash equilibria in optimal taxation problems

Krastanov

Rozenov²

2009

Open Mathematics

View full text Add to dashboard Cite

Abstract:A well-known result in public economics is that capital income should not be taxed in the long run. This result has been derived using necessary optimality conditions for an appropriate dynamic Stackelberg game. In this paper we consider three models of dynamic taxation in continuous time and suggest a method for calculating their feedback Nash equilibria based on a sufficient condition for optimality. We show that the optimal tax on capital income is generally different from zero. MSC:91A23, 91A65, 91B64, 49K15

show abstract

“…, then the Hamiltonian function H(t, X(t), U(t), P(t)) is a convex function in (X(t), U(t)) for t ∈ [t 0 , t f ] (we need nonnegativity of the costate variables only for those components of f (t, X(t), U(t)) that are nonlinear in X(t) [18,19] …”

Section: Appendix Bmentioning

confidence: 99%

Dynamic routing and admission control for virtual circuit networks

1995

View full text Add to dashboard Cite

The dynamic joint routing and admission control problem in multiple class multiple source-destination virtual circuit networks is considered.A nonlinear dynamic queueing model for virtual circuit networks that considers the dynamic interaction among the virtual circuit and packet processes is introduced. Then a multi-objective cost function of rejecting & maintaining virtual circuits, as well as of delaying & servicing packets is defined.The combined problem is formulated as an optimal control problem. Necessary optimality conditions are provided by Pontryagin's maximum principle. Sufficient optimality conditions based on the convexity of the Hamiltonian function are also given. For the finite horizon, the optimal controls can be found after numerically solving a Two-Point Boundary-Value Problem. For the long-run stationary equilibrium, the state-dependent routing and admission controls are derived.

show abstract

Sufficient Conditions in Optimal Control Theory

Cited by 285 publications

References 11 publications

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

Feedback Nash equilibria in optimal taxation problems

Dynamic routing and admission control for virtual circuit networks

Contact Info

Product

Resources

About