1,660 research outputs found
Value Functions and Transversality Conditions for Infinite-Horizon Optimal Control Problems
This paper investigates the relationship between the maximum principle with an infinite horizon and dynamic programming and sheds new light upon the role of the transversality condition at infinity as necessary and sufficient conditions for optimality with or without convexity assumptions. We first derive the nonsmooth maximum principle and the adjoint inclusion for the value function as necessary conditions for optimality that exhibit the relationship between the maximum principle and dynamic programming. We then present sufficiency theorems that are consistent with the strengthened maximum principle, employing the adjoint inequalities for the Hamiltonian and the value function. Synthesizing these results, necessary and sufficient conditions for optimality are provided for the convex case. In particular, the role of the transversality conditions at infinity is clarified
Necessity of vanishing shadow price in infinite horizon control problems
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 there was suggested the boundary condition for equations of the
Pontryagin Maximum Principle. Each optimal process corresponds to a unique
solution satisfying the boundary condition. Following A.Seierstad's idea, in
this paper we prove a more general geometric variety of that boundary
condition. We show that this condition is necessary for uniformly overtaking
optimal control on infinite horizon in the free end case. A number of
assumptions under which this condition selects a unique Lagrange multiplier is
obtained. The results are applicable to general non-stationary systems and the
optimal objective value is not necessarily finite. Some examples are discussed
Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
We consider problems of the calculus of variations on unbounded time scales.
We prove the validity of the Euler-Lagrange equation on time scales for
infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for
publication in "Optimization Letters"
Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales
We obtain Euler-Lagrange and transversality optimality conditions for
higher-order infinite horizon variational problems on a time scale. The new
necessary optimality conditions improve the classical results both in the
continuous and discrete settings: our results seem new and interesting even in
the particular cases when the time scale is the set of real numbers or the set
of integers.Comment: This is a preprint of a paper whose final and definite form will
appear in Journal of Optimization Theory and Applications (JOTA). Paper
submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for
publication 15-April-201
- …