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1.
In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge–Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.  相似文献   

2.
In this paper, we applied the finite differences method to the solution of variational problem of an inverse problem for the Scrödinger equation with a final functional. These types of problems arise in various fields in quantum-mechanical, nuclear physics and modern physics [2, 11]. Also, we prove two estimates for the differences scheme and convergence speed of difference approximations according to the functional. The inverse problems for the Schrödinger equation having different variational formulation were investigated in [7, 12, 13].  相似文献   

3.
In this paper we study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor, with finite and infinite time horizon. We assume that harvest is restricted to mature trees older than a certain age and that growth and natural mortality after maturity are neglected. We use stochastic dynamic programming techniques to characterize the optimal policy and we model price using a geometric Brownian motion and an Ornstein–Uhlenbeck process. In the first case we completely characterize the optimal policy for all possible choices of the parameters. In the second case we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. In addition, for the Ornstein–Uhlenbeck case we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained endogenously, that is, without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state.  相似文献   

4.
We give a new criterion for the existence of value in differential games. The method of proof involves Lipschitz differential games and hence extends to games with more general dynamics. The connection between using measurable control functions or simply constants is clarified.  相似文献   

5.
We study the problem of selecting one of the r best of n rankable individuals arriving in random order, in which selection must be made with a stopping rule based only on the relative ranks of the successive arrivals. For each r up to r=25, we give the limiting (as n→∞) optimal risk (probability of not selecting one of the r best) and the limiting optimal proportion of individuals to let go by before being willing to stop. (The complete limiting form of the optimal stopping rule is presented for each r up to r=10, and for r=15, 20 and 25.) We show that, for large n and r, the optical risk is approximately (1−t*)r, where t*≈0.2834 is obtained as the roof of a function which is the solution to a certain differential equation. The optimal stopping rule τr,n lets approximately t*n arrivals go by and then stops ‘almost immediately’, in the sense that τr,n/nt* in probability as n→∞, r→∞  相似文献   

6.

In this paper, we study a problem of optimal harvesting from a stochastic system modeled by a geometric Lévy process. A verification theorem of the variational inequality type is also given and proved. The paper has been motivated by I. Elsanosi et al. [Stochastics Stochastics Rep. (2000)], where the authors considered an optimal harvesting problem with price dynamics following a stochastic differential delay equation.  相似文献   

7.
An algorithm optimal in order is proposed for solving an inverse Stefan problem. We also give some exact estimates of accuracy of this method.  相似文献   

8.
A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinations according to the features of the tasks. A weighted routing tree is one with costs attached to each link of the tree. Links of the same feature have the same cost. It is proved that the problem of finding a routing tree of the minimum cost for a given set of tasks of two features is NP-complete.This research was supported in part by theNSF grantsDCR-8501226 andDCR-8696135. Part of this work was done while the first author was at the Mathematical Sciences Research Institute, Berkeley, California, and while the second author was at the Department of Mathematics, University of California, Santa Barbara, California.  相似文献   

9.
This article is concerned with a dynamic blocking problem, originally motivated by the control of wild fires. It is assumed that the region ${R(t) \subset \mathbb {R}^2}$ burned by the fire is initially a disc, and expands with unit speed in all directions. To block the fire, a barrier Γ can be constructed in real time, so that the portion of the barrier constructed within time t has length ≤? σt, for some constant σ >? 2. We prove that, among all barriers consisting of a single closed curve, the one which minimizes the total burned area is axisymmetric, and consists of an arc of circumference and two arcs of logarithmic spirals.  相似文献   

10.
This work is concerned with a kind of optimal control problem for a size-structured biological population model. Well-posedness of the state system and an adjoint system are proved by means of Banach’s fixed point theorem. Existence and uniqueness of optimal control are shown by functional analytical approach. Optimality conditions describing the optimal strategy are established via tangent and normal cones technique. The results are of the first ones for this novel structure.  相似文献   

11.
The correctness of the problem of optimal control by the coefficients for a weakly nonlinear hyperbolic equation is studied, and a necessary condition of optimality is established.  相似文献   

12.
Mathematical Notes - This paper studies the optimality in the problem of cyclic harvesting of a resource distributed on a circle with a certain prescribed density. The velocity ofmotion of the...  相似文献   

13.
We are the first solve the optimization problem for a boundary displacement control of string vibrations at one endpoint in the case of a nonstationary boundary condition containing a directional derivative at the other endpoint.  相似文献   

14.
Existence of solutions is proved for a minimum problem for a distributed-parameter control system described by a linear, hyperbolic partial differential equation. The cost function is an integral depending on boundary controls.This research was supported by the Consiglio Nazionale delle Ricerche, Rome, Italy.  相似文献   

15.
L.A. Shepp has posed and analyzed the problem of optimal random drawing without replacement from an urn containing predetermined numbers of plus and minus balls. Here Shepp's results are extended by improving the bounds on values of perturbed urns, deriving an exact algorithm for the urn values and computing the stopping boundary for urns of up to 200 balls.  相似文献   

16.
In a recent paper (Ref. 1), Cheng and Teo discussed some further extensions of a student-related optimal control problem which was originally proposed by Raggettet al. (Ref. 2) and later on modified by Parlar (Ref. 3). In this paper, we treat further extensions of the problem.This paper is a modified and improved version of Ref. 4. It is based, in part, on research sponsored by NSF.  相似文献   

17.
18.
Summary A class of one-dimensional search problems is considered. The formulation results in a functional-minimization equation of the dynamic programming type. In the case of a uniform a priori distribution for the location of the hidden object an optimality criterion is established and the optimal search procedure is found.
Zusammenfassung Nach allgemeinen Betrachtungen über das Spektrum von Suchproblemen wird eine Klasse eindimensionaler Suchprobleme betrachtet. Die Formulierung führt zu einer Funktionalgleichung vom Typ der dynamischen Optimierung. In dem Fall einer uniformen a priori Verteilung für das Auffinden eines versteckten Objekts wird ein Optimalitätskriterium begründet und das optimale Suchverfahren angewandt.
  相似文献   

19.
We present the solution of an optimization problem with integral performance functional that is nonlinear with respect to the control and contains a discounting parameter in the class of programmed controls under two-sided control constraints. The optimal control is found in the form of a function of time (a program). On the basis of the theoretical results, we perform numerical experiments with model and real data.  相似文献   

20.
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